$H_{\infty}$ Controller Design for Singular Stochastic Markovian Jump System With Time-Varying Delay

Abstract

This considers the problem of H ∞ controller design for singular stochastic systems. The systems have Markovian jump and time-varying delay. We aim to design a controller ensuring the closed-loop system is stochastically admissible and satisfies a prescribed H ∞ performance index γ . Based on the linear matrix inequalities (LMIS) techniques, the mode-dependent singular matrices E (r t ) and the stochastic Lyapunov function method, a sufficient condition for the desired H ∞ controller for the system under consideration is given in terms of LMIs. Moreover, to clarify the proposed results, some illustrative examples are presented.INDEX TERMS Singular stochastic system, linear matrix inequality, H ∞ control, time-varying delays, Lyapunov-Krasovskii functional.

Observer-based H∞ control for uncertain one-sided Lipschitz Markovian jump-delayed systems with partially unknown transition rates

“…Definition 1: The system (1) with w ( t ) = 0 is said to be stochastically stable if for any x 0 ∈ R n and r 0 ∈ S , there exists a scalar M ~ ( x ( 0 ) , r 0 ) (Du et al, 2019)…”

“…Definition 2: Given a scalar γ > 0 ,the system (1) is said to be stochastically stable with an H ∞ performance level γ if it is stochastically stable with w ( t ) = 0 and under the initial condition, for nonzero w ( t ) ∈ L 2 [ 0 , ∞ ) (Du et al, 2019)…”

Delay-Dependent H∞ Control for Singular Markovian Jump Systems With Generally Uncertain Transition Rates

“…An effective method is to use Markov process to describe such phenomena and model the system as a SMJSs, and then a controller is designed to eliminate the influence of these random factors. In recent years, considerable attention has been paid to the stability analysis, controller synthesis, and filtering problems of SMJSs, see [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], and the references therein.…”

Stabilization and Event-Triggered Control of Stochastic Delay Systems With Markovian Jump Parameters

“…In effect, the above affect factors often give rise to oscillation, poor performance and even instability. As a hot issue in the study of STDSs, stability analysis has aroused wide concerns among many investigators (see, e.g., [1]- [5]), and it is the primary task for researchers to discuss how to construct a controller to stabilize an unstable controlled system (see, e.g., [6]- [8]).…”