Search results for "delta operator"

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

2014

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 …

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

2014

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

2014

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 …

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

2014

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 …

Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

2013

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/913234 Open Access The stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii funct…

Stability of genetic regulatory networks with time-varying delay: Delta operator method

2015

This paper investigates the stability problem for a class of uncertain genetic regulatory networks (GRNs) with time-varying delay via delta operator approach. Both the parameter uncertainty and the generalized activations are considered in the model under study. By constructing an appropriate Lyapunov-Krasovskii functional, the stability and robust stability conditions of GRNs are presented under the delta operator frame. These conditions can be expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is employed to illustrate the effectiveness of the proposed results.

Control Design for Discrete-Time Fuzzy Systems with Disturbance Inputs via Delta Operator Approach

2013

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher: http://dx.doi.org/10.1155/2013/724918 Open Access This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a st…

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

2014

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

2013

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…

Approximation Operators of Binomial Type

1999

Our objective is to present a unified theory of the approximation operators of binomial type by exploiting the main technique of the so- called “ umbral calculus” or “finite operator calculus” (see [18], [20]-[22]). Let us consider the basic sequence (bn)n≥0 associated to a certain delta operator Q. By supposing that b n (x) ≥ 0, x ∈ [0, ∞), our purpose is to put in evidence some approximation properties of the linear positive operators (L Q n ) n≥1 which are defined on C[0,1] by \( L_n^Qf = \sum\limits_{k = 0}^n {\beta _n^Q{,_k}f\left( {\frac{k}{n}} \right),\beta _{n{,_k}}^Q\left( x \right): = } \frac{1}{{{b_n}\left( n \right)}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right){b_…