Robust l2-gain control for 2D nonlinear stochastic systems with time-varying delays and actuator saturation

Abstract This paper is concerned with the problems of stability analysis and l2-gain control for a class of two-dimensional (2D) nonlinear stochastic systems with time-varying delays and actuator saturation. Firstly, a convex hull representation is used to describe the saturation behavior, and a sufficient condition for the existence of mean-square exponential stability of the considered system is derived. Then, a state feedback controller which guarantees the resulting closed-loop system to be mean-square exponentially stable with l2-gain performance is proposed, and an optimization procedure to maximize the estimation of domain of attraction is also given. All the obtained results are for…

Delay-dependent exponential stabilization of positive 2D switched state-delayed systems in the Roesser model

This paper deals with the controller synthesis for a class of positive two-dimensional (2D) switched delay systems described by the Roesser model. This kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative, some delay-dependent sufficient conditions for the exponential stability of positive 2D switched systems with state delays are given. Furthermore, the design of positive state feedback controller under which the resulting closed-loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities (LMIs). An example is included to illustrate the effectiveness of the…

Stability and -gain controller design for positive switched systems with mixed time-varying delays

This paper investigates the problems of stability and L"1-gain controller design for positive switched systems with mixed time-varying delays. The mixed time-varying delays are presented in the forms of discrete delay and distributed delay. The purpose of this paper is to design a class of switching signals and a state feedback controller for the considered system such that the resulting closed-loop system is exponentially stable with L"1-gain performance. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and using the average dwell time approach, we propose a sufficient condition to ensure the exponential stability with weighted L"1-gain performance for the sys…

Finite-Timel1-Gain Control for Positive Switched Systems with Time-Varying Delay via Delta Operator Approach

This paper is concerned with the problem of finite-timel1-gain control for positive switched systems with time-varying delay via delta operator approach. Firstly, sufficient conditions which can guarantee thel1-gain finite-time boundedness of the underlying system are given by using the average dwell time approach and constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant results seen in literature of both continuous and discrete systems into the delta operator framework. Then, based on the results obtained, a state feedback controller is designed to ensure that the resulting …

Asynchronous L1 control of delayed switched positive systems with mode-dependent average dwell time

Abstract This paper investigates the stability and asynchronous L 1 control problems for a class of switched positive linear systems (SPLSs) with time-varying delays by using the mode-dependent average dwell time (MDADT) approach. By allowing the co-positive type Lyapunov–Krasovskii functional to increase during the running time of active subsystems, a new stability criterion for the underlying system with MDADT is first derived. Then, the obtained results are extended to study the issue of asynchronous L 1 control, where “asynchronous” means that the switching of the controllers has a lag with respect to that of system modes. Sufficient conditions are provided to guarantee that the resulti…

Robust fault detection for switched systems with time-varying delay using delta operator approach

Delay-dependent control for 2-D switched delay systems in the second FM model

This paper is concerned with the problem of delay-dependent H∞ control for 2-D (two-dimensional) switched discrete state delay systems described by the second FM (Fornasini and Marchesini) state-space model. Firstly, some sufficient conditions for the exponential stability and weighted H∞ disturbance attenuation performance of the underlying system are derived via the average dwell time approach. Then, based on the obtained results, a state feedback controller design is proposed to guarantee that the resulting closed-loop system is exponentially stable and achieves a prescribed disturbance attenuation level γ. Finally, a numerical example is provided to verify the effectiveness of the propo…

Robust H∞ reliable control for delta operator switched systems with time-varying delays under asynchronous switching

The problem of robust H∞ reliable control for a class of delta operator switched systems with time-varying delays and actuator faults under asynchronous switching is considered in this paper. Asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. Based on the average dwell time approach and delta operator theory, a state feedback controller is designed such that the closed-loop system is exponentially stable with H∞ performance in the presence of actuator faults. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate explicitly the feasibility …

Robust reliable control of uncertain discrete impulsive switched systems with state delays

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/197819 Open access This paper is concerned with the problem of robust reliable control for a class of uncertain discrete impulsive switched systems with state delays, where the actuators are subjected to failures. The parameter uncertainties are assumed to be norm-bounded, and the average dwell time approach is utilized for the stability analysis and controller design. Firstly, an exponential stability criterion is established in terms of linear matrix inequalities (LMIs). Then, a state feedback controller is constructed for the underlyin…

Mixed l-/l1 fault detection observer design for positive switched systems with time-varying delay via delta operator approach

Published version of an article in the journal: International Journal of Control, Automation and Systems. Also available from the publisher at: http://dx.doi.org/10.1007/s12555-013-0466-1 This paper investigates the problem of fault detection observer design for positive switched systems with time-varying delay via delta operator approach. A new fault sensitivity measure, called l-index, is proposed. The l- fault detection observer design and multi-objective l -/l1 fault detection observer design problems are addressed. Based on the average dwell time approach and the piecewise copositive type Lyapunov-Krasovskii functional method in delta domain, sufficient conditions for the existence of …

Finite-time l1-gain control for positive switched systems with time-varying delay via delta operator approach

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/872158 Open Access This paper is concerned with the problem of finite-time l 1 -gain control for positive switched systems with time-varying delay via delta operator approach. Firstly, sufficient conditions which can guarantee the l 1 -gain finite-time boundedness of the underlying system are given by using the average dwell time approach and constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant results seen in literature of both …

Stability and l1-gain analysis for positive 2D T–S fuzzy state-delayed systems in the second FM model

This paper considers the problems of delay-dependent stability and l"1-gain analysis for a class of positive two-dimensional (2D) Takagi-Sugeno (T-S) fuzzy linear systems with state delays described by the second FM model. Firstly, the co-positive type Lyapunov function method is applied to establish sufficient conditions of asymptotical stability for the addressed positive 2D T-S fuzzy system. Then, the l"1-gain performance analysis for the positive 2D T-S fuzzy delayed system is studied. All the obtained results are formulated in the form of linear matrix inequalities (LMIs) which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the p…

Stabilization and lx -gain analysis of switched positive systems with actuator saturation

This paper is concerned with the problems of stability and l 1 -gain analysis for a class of switched positive systems with time-varying delays and actuator saturation. Firstly, a convex hull representation is used to describe the saturation behavior. By constructing a multiple co-positive Lyapunov functional, sufficient conditions are provided for the closed-loop system to be locally asymptotically stable at the origin of the state space under arbitrary switching. Then, the l 1 -gain performance analysis in the presence of actuator saturation is developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

Positive L1 observer design for positive Switched systems

Published version of an article in the journal: Circuits, Systems, and Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1007/s00034-013-9737-6 This paper investigates the problem of L1 observer design for positive switched systems. Firstly, a new kind of positive L1 observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive L1 observer. Under the condition obtained, the estimated error converges to zero exponentially, and the L1 -gain from the disturbance input to the estimated error is less t…

Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays

Published version of an article in the journal: Circuits, Systems, and Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1007/s00034-013-9610-7 This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for discrete impulsive switched systems with state delays. Sufficient conditions are presented for the existence of IO-FTS for such systems under the cases of certain switching, arbitrary switching, and uncertain switching. All the obtained results are formulated in a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed results.

Output Feedback Control of Discrete Impulsive Switched Systems with State Delays and Missing Measurements

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/283426 Open Access This paper is concerned with the problem of dynamic output feedback (DOF) control for a class of uncertain discrete impulsive switched systems with state delays and missing measurements. The missing measurements are modeled as a binary switch sequence specified by a conditional probability distribution. The problem addressed is to design an output feedback controller such that for all admissible uncertainties, the closed-loop system is exponentially stable in mean square sense. By using the average dwell time approach a…

Stability andl1-Gain Analysis for Positive 2D Systems with State Delays in the Roesser Model

This paper considers the problem of delay-dependent stability andl1-gain analysis for positive 2D systems with state delays described by the Roesser model. Firstly, the copositive-type Lyapunov function method is used to establish the sufficient conditions for the addressed positive 2D system to be asymptotically stable. Then,l1-gain performance for the system is also analyzed. All the obtained results are formulated in the form of linear matrix inequalities (LMIs) which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the proposed results.

Asynchronously switched control of discrete impulsive switched systems with time delays

This paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By using the average dwell time (ADT) approach, sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed-loop system is exponentially stable. The desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.

Positive l<inf>1</inf> observer design for positive switched systems with time-varying delays via delta operator approach

H-infinity control for networked control systems with time delays and packet dropouts

Published version of an article from the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2013/635941 This paper is concerned with the H-infinity control issue for a class of networked control systems (NCSs) with packet dropouts and time-varying delays. Firstly, the addressed NCS is modeled as a Markovian discrete-time switched system with two subsystems; by using the average dwell time method, a sufficient condition is obtained for the mean square exponential stability of the closed-loop NCS with a desired H-infinity disturbance attenuation level. Then, the desired H-infinity controller is obtained by solving a set of linear matrix inequ…

Stability and -Gain Control of Positive Switched Systems with Time-Varying Delays via Delta Operator Approach

This paper investigates the problems of stability and -gain controller design for positive switched systems with time-varying delays via delta operator approach. The purpose is to design a switching signal and a state feedback controller such that the resulting closed-loop system is exponentially stable with -gain performance. Based on the average dwell time approach, a sufficient condition for the existence of an -gain controller for the considered system is established by constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant methods in the literature of both continuous- and…

Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities

This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired…

Input-output finite-time stability of positive switched linear systems with state delays

This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for a class of discrete-time positive switched systems with time-varying delays. Two sufficient conditions for the existence of IO-FTS of such systems with respect to two different input signals are presented, respectively. All the results obtained are formulated in a set of linear inequalities. Two numerical examples are given to illustrate the effectiveness of the proposed results.

Stabilization of positive switched systems with time-varying delays under asynchronous switching

Published version of an article in the journal: International Journal of Control, Automation and Systems. Also available from the publisher at: http://dx.doi.org/10.1007/s12555-013-0486-x This paper investigates the state feedback stabilization problem for a class of positive switched systems with time-varying delays under asynchronous switching in the frameworks of continuous-time and discrete-time dynamics. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and further allowing the functional to increase during the running time of ac…

Delay-Dependent Control for Networked Control Systems with Large Delays

We consider the problems of robust stability and control for a class of networked control systems with long-time delays. Firstly, a nonlinear discrete time model with mode-dependent time delays is proposed by converting the uncertainty of time delay into the uncertainty of parameter matrices. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of linear matrix inequalities (LMIs). Then, we extend the results to a more practical case where the …

Dynamic Output Feedback Passive Control of Uncertain Switched Stochastic Systems with Time-Varying Delay

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2013/281747 Open Access This paper is concerned with the issues of passivity analysis and dynamic output feedback (DOF) passive control for uncertain switched stochastic systems with time-varying delay via multiple storage functions (MSFs) method. Firstly, based on the MSFs method, a sufficient condition for the existence of the passivity of the underlying system is established in terms of linear matrix inequalities (LMIs). Furthermore, the problem of dynamic output feedback passive control is investigated. Based on the obtained passivity condition, a …

Stabilization and controller design of 2D discrete switched systems with state delays under asynchronous switching

Published version of a paper from the journal: Abstract and Applied Analysis. Also available from Hindawi:http://dx.doi.org/10.1155/2013/961870. Open Access This paper is concerned with the problem of robust stabilization for a class of uncertain two-dimensional (2D) discrete switched systems with state delays under asynchronous switching. The asynchronous switching here means that the switching instants of the controller experience delays with respect to those of the system. The parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee the exponential stability. The dwell time approach is utilized for the stability analysis and controller …

Control for Networked Control Systems with Time Delays and Packet Dropouts

This paper is concerned with the control issue for a class of networked control systems (NCSs) with packet dropouts and time-varying delays. Firstly, the addressed NCS is modeled as a Markovian discrete-time switched system with two subsystems; by using the average dwell time method, a sufficient condition is obtained for the mean square exponential stability of the closed-loop NCS with a desired disturbance attenuation level. Then, the desired controller is obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Design of a robust H<inf>∞</inf> repetitive control system with time-delay

Delay-dependent H-infinity control for networked control systems with large delays

Published version of an article from the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2013/643174 We consider the problems of robust stability and H-infinity control for a class of networked control systems with long-time delays. Firstly, a nonlinear discrete time model with mode-dependent time delays is proposed by converting the uncertainty of time delay into the uncertainty of parameter matrices. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. For a switched system with a known subsystem occurrence …

Observer-Based ${H}_{\infty }$ Control Design for Nonlinear Networked Control Systems with Limited Information

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/604249 Open Access This paper is concerned with the problem of designing a robust observer-based H∞ controller for discrete-time networked systems with limited information. An improved networked control system model is proposed and the effects of random packet dropout, time-varying delay, and quantization are considered simultaneously. Based on the obtained model, a stability criterion is developed by constructing an appropriate Lyapunov-Krasovskii functional and sufficient conditions for the existence of a dynamic quantized output feedback cont…

Robust sampled-data H∞ control for vibration mitigation of offshore platforms with missing measurements

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2014/914616 This paper presents a robust sampled-data H ∞ control for vibration attenuation of offshore platforms with missing measurements subject to external wave force. It is well known that the phenomena of missing measurements are unavoidable due to various reasons, such as sensor aging and sensor temporal failure, which may degrade the control system performance or even cause instability. For active vibration control of offshore platforms with sampling measurements, to deal with the missing measurements, a robust sampled-data H ∞ control…

Robust Switching Rule Design for Boost Converters with Uncertain Parameters and Disturbances

Pubished version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/120543 Open access This paper is concerned with the design problem of robust H∞ switching rule for Boost converters with uncertain parameters and disturbances. Firstly, the Boost converter is modeled as a switched affine linear system with uncertain parameters and disturbances. Then, using common Lyapunov function approach and linear matrix inequality (LMI) technique, a novel switching rule is proposed such that the H∞ model reference tracking performance is satisfied. Finally, a simulation result is provided to show the validity of the proposed …

Observer-Based Robust Control for Switched Stochastic Systems with Time-Varying Delay

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/320703 Open Access This paper investigates the problem of observer-based robust H ∞ control for a class of switched stochastic systems with time-varying delay. Based on the average dwell time method, an exponential stability criterion for switched stochastic delay systems is proposed. Then, H ∞ performance analysis and observer-based robust H ∞ controller design for the underlying systems are developed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

Disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator

Abstract This paper is concerned with the problems of disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator. Using the switched Lyapunov function approach, a sufficient condition for the existence of a state feedback controller is proposed such that the disturbance tolerance capability of the closed-loop system is ensured. By solving a convex optimization problem with linear matrix inequality (LMI) constraints, the maximal disturbance tolerance is estimated. In addition, the problem of disturbance rejection of the closed-loop system is solved. Two examples are given to illustrate the effectiveness of the proposed method.

Robust reliable passive control of uncertain stochastic switched time-delay systems

This paper investigates the problem of robust reliable passive control for a class of uncertain stochastic switched time-delay systems with actuator failures. The multiple Lyapunov functions (MLFs) technique is exploited to derive a delay-dependent sufficient condition for the stochastic switched time-delay systems to be passive and exponentially stable under a state-based switching law. Moreover, the proposed approach is extended to investigate stochastic switched systems with structured uncertainties. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method.