H_∞ controller design for singular Markov jump systems with time-delays

Abstract

In this article, the [Formula: see text] control problem of a class of singular Markov jump systems with time-varying inputs and state delays is investigated. Based on the Lyapunov stability theory, by constructing a different Lyapunov–Krasovskii functional, the sufficient conditions of being stochastic stable and having H∞ performance index are given. Then, the design method of state feedback controller is given to ensure the closed-loop system is stochastic stable and has [Formula: see text] performance index. Finally, simulation examples are given to verify the effectiveness of the proposed methods.

Synthesis of H∞ Control for Descriptor Hybrid Systems with Actuator Saturation

“…Then the condition (20) is equivalent to (23) through the relation (29). Next, to reformulate the condition (21) as (24), we will employ the following full-rank matrix:…”

“…In the view of optimal control, LMIs have been widely employed due to their ease in finding optimal solutions. In the case of H ∞ control for DHSs, research usually started from the stochastic admissibility criterion with H ∞ performance γ [23][24][25]. This criterion, if both necessary and sufficient, is commonly referred to as the bounded real lemma [26].…”

Asynchronous control for Markov jump systems subject to actuator saturation and partial mode information

“…Based on closed-loop hidden MJSs (7) and condition x(k) 2 L(H), the control target is to find the largest set that all initial states starting from it can remain in it totally and trend to the origin. Before proposing the detail design procedure, we introduce the following concept of stochastic stability.…”

“…5 A model-free adaptive optimal control policy for discrete-time MJSs was developed in the works of Zhou et al 6 The H ' control problem of a class of singular MJSs with timevarying inputs and state delays was investigated. 7 Furthermore, in the control field, actuator saturation is an undesired phenomenon, which results from physical limitations and may degrade the performance of systems, even cause systems to become unstable. Actuator saturation was handled by regarding as a locally sector bounded nonlinearity.…”

“…5 A model-free adaptive optimal control policy for discrete-time MJSs was developed in the works of Zhou et al 6 The H ∞ control problem of a class of singular MJSs with time-varying inputs and state delays was investigated. 7…”