H∞ control for two-dimensional Markovian jump systems with state-delays and defective mode information

This paper investigates the problem ofℋ∞state-feedback control for a class of two-dimensional (2D) discrete-time Markovian jump linear time-delay systems with defective mode information. The mathematical model of the 2D system is established based on the well-known Fornasini-Marchesini local state-space model, and the defective mode information simultaneously consists of the exactly known, partially unknown, and uncertain transition probabilities. By carefully analyzing the features of the transition probability matrices, together with the convexification of uncertain domains, a newℋ∞performance analysis criterion for the underlying system is firstly derived, and then theℋ∞state-feedback co…

Setpoints compensation in industrial processes via multirate output feedback control

This paper investigates the setpoints compensation for a class of complex industrial processes. Plants at the device layer are controlled by the local regulation controllers, and a multirate output feedback control approach for setpoint compensation is proposed such that the subsystems can reach the dynamically changed setpoints and the given economic objective can also be tracked via certain economic performance index (EPI). First, a sampled-data multivariable direct output feedback proportional integral (PI) controller is designed to regulate the performance of the subsystems. Second, the outputs and control inputs of the plants at the device layer are sampled at operation layer sampling …

Memory ℋ<inf>∞</inf> control for continuous-time Markovian jump systems with time-varying delay and defective mode information

New results on H∞ dynamic output feedback control for Markovian jump systems with time-varying delay and defective mode information

SUMMARY This paper investigates the problem of delay-dependent H∞ dynamic output feedback control for a class of discrete-time Markovian jump linear systems (MJLSs). The systems under consideration are subject to time-varying delay and defective mode information. The defective transition probabilities comprise of three types: exactly known, uncertain, and unknown. By employing a two-term approximation for the time-varying delay, the original MJLSs can be equivalently converted into a feedback interconnection form, which contains a forward subsystem with constant time-delays and a feedback one with norm-bounded uncertainties. Then, based on the scaled small-gain theorem, the problem is there…

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

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…

Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information

This paper is concerned with the problem of H"~ filtering for a class of two-dimensional Markovian jump linear systems described by the Fornasini-Marchesini local state-space model. The systems under consideration are subject to state-delays and deficient mode information in the Markov chain. The description of deficient mode information is comprehensive that simultaneously includes the exactly known, partially unknown and uncertain transition probabilities. By invoking the properties of the transition probability matrix, together with the convexification of uncertain domains, a new H"~ performance analysis criterion for the filtering error system is firstly derived. Then, via some matrix i…

A new design of H ∞ filtering for continuous-time Markovian jump systems with time-varying delay and partially accessible mode information

In this paper, the delay-dependent H"~ filtering problem for a class of continuous-time Markovian jump linear systems with time-varying delay and partially accessible mode information is investigated by an indirect approach. The generality lies in that the systems under consideration are subject to a Markov stochastic process with exactly known and partially unknown transition rates. By utilizing the model transformation idea, an input-output approach is employed to transform the time-delayed filtering error system into a feedback interconnection formulation. Invoking the results from the scaled small gain theorem, an improved version of bounded real lemma is obtained based on a Markovian L…

New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions

Abstract This paper proposes an input–output (IO) approach to the delay-dependent stability analysis and H ∞ controller synthesis for a class of continuous-time Markovian jump linear systems (MJLSs). The concerned systems are with a time-varying delay in the state and deficient mode information in the Markov stochastic process, which simultaneously involves the exactly known, partially unknown and uncertain transition rates. It is first shown that the original system with time-varying delay can be reformulated by a new IO model through a process of two-term approximation and the stability problem of the original system can be transformed into the scaled small gain (SSG) problem of the IO mo…

model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information

This paper investigates the problem of model reduction for a class of continuous-time Markovian jump linear systems with incomplete statistics of mode information, which simultaneously considers the exactly known, partially unknown and uncertain transition rates. By fully utilising the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for performance analysis is first derived, and then two approaches, namely, the convex linearisation approach and the iterative approach, are developed to solve the model reduction problem. It is shown that the desired reduced-order models can be obtained by solving a set of strict linear…

Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information

Published version of an article in the journal: Multidimensional Systems and Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1007/s11045-013-0276-x This paper is concerned with the problem of {Mathematical expression} model approximation for a class of two-dimensional (2-D) discrete-time Markovian jump linear systems with state-delays and imperfect mode information. The 2-D system is described by the well-known Fornasini-Marchesini local state-space model, and the imperfect mode information in the Markov chain simultaneously involves the exactly known, partially unknown and uncertain transition probabilities. By using the characteristics of the transition proba…

H∞ model reduction for discrete-time Markovian jump systems with deficient mode information

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/537174 Open Access This paper investigates the problem of H∞ model reduction for a class of discrete-time Markovian jump linear systems (MJLSs) with deficient mode information, which simultaneously involves the exactly known, partially unknown, and uncertain transition probabilities. By fully utilizing the properties of the transition probability matrices, together with the convexification of uncertain domains, a new H∞ performance analysis criterion for the underlying MJLSs is first derived, and then two approaches, namely, the convex li…