H∞ control of Markov jump time-delay systems under asynchronous controller and quantizer

Abstract

This paper aims to design an asynchronous state feedback controller for Markov jump time-delay systems. The highlight of this work lies in that the state feedback is quantized by a logarithmic quantizer, and both the controller and quantizer are asynchronous with the controlled systems. By Lyapunov-Krasovskii functional, a sufficient condition is presented to ensure that the resulting closed-loop system is stochastically mean square stable with a prescribed H∞ performance index. Finally, an example is presented to illustrate the effectiveness and new features of proposed design method.

Strictly dissipative stabilization of multiple‐memory Markov jump systems with general transition rates: A novel event‐triggered control strategy

“…By using Schur Complement to (12) and (13), one can obtain from (A18) and (A19) that { V(x(t), t, (t))+ (t)} < 0. If i ∉  i 1 and  i 2 ≠ , there exist P i − P j ≥ 0 ( ∈  i 2 , ≠ i), one has…”

“…In addition, time delays, which generally lead to undesirable situations including instability and oscillation of a system, are unavoidably encountered in signal transmission . Hence, to stabilize MJSs with time delays is important, and many interesting results have been reported . However, the transition rates (TRs) of all modes were assumed to be completely known or partially known.…”

“…[7][8][9] Hence, to stabilize MJSs with time delays is important, and many interesting results have been reported. [10][11][12][13][14] However, the transition rates (TRs) of all modes were assumed to be completely known or partially known. In practice, owing to certain technical restriction and the influence of uncertain factors, all TRs of some jumping modes may be completely unknown, which leads to a circumstance that the existing results are incapable to solve some practical problems.…”

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

“…20,27,28 For instance, in the work of Khajeh Talkhoncheh, 29 they developed an observer-based adaptive neural controller for a class of strict-feedback nonlinear systems subjected to unknown control directions, saturation, and input time delay, which is handled by using an integrator compensator term in the controller design. [30][31][32][33] Recently, Shen et al, 33 have proposed an asynchronous state feedback controller for Markovian jump time-delay systems by using Lyapunov-Krasovskii functional, and Que et al 31 have investigated a new globally exponentially synchronization criterion for complex dynamical networks by considering time delay. 27 Constructing appropriate Lyapunov-Krasovskii functions is another approach to cancel the unknown time-delay terms.…”

“…20,28 Recently, using time-varying delays in control design of discrete complex systems has received a great deal of attention. [30][31][32][33] Recently, Shen et al, 33 have proposed an asynchronous state feedback controller for Markovian jump time-delay systems by using Lyapunov-Krasovskii functional, and Que et al 31 have investigated a new globally exponentially synchronization criterion for complex dynamical networks by considering time delay.…”