Abstract
This article is concerned with the problem of resilient asynchronous H∞ static output feedback control for discrete-time Markov jump linear systems. By Finsler’s Lemma, and with the help of two sets of slack variables, the product terms of system matrices and Lyapunov matrices are decoupled. Resilient asynchronous controller is designed to improve the robustness of the controller and overcome the drawback that the controller cannot get the information of the system’s mode. The controller that makes sure the closed-loop system is stochastically stable and with prescribed H∞ performance is designed. The bilinear matrix inequalities are given as the sufficient conditions for the controller design, which can be solved using linear matrix inequalities along with line search. This control strategy can be used in many practical application fields, such as robot control, aircraft, and traffic control.
Highlights
Because of the impact of external environment, internal failure, the communication delay such as considered in Lu et al.,[1] the noise such as considered in Lu et al.,[2] and other reasons, most of the subjects to be described are dynamic and time-variant
Markov chain determines the different modes in the Markov jump linear systems (MJLSs)
Economic systems are described by MJLSs in Zhao and Zhang.[6]
Summary
Because of the impact of external environment, internal failure, the communication delay such as considered in Lu et al.,[1] the noise such as considered in Lu et al.,[2] and other reasons, most of the subjects to be described are dynamic and time-variant. The discrete-time MJLSs and the resilient asynchronous HN static output feedback controller is formulated, and several essential definitions and lemmas are given in section ‘‘Preliminaries and problem formulation.’’ Based on these lemmas and definitions, the controller designed for the closed-loop system makes sure the system has a prescribe HN performance index and is stochastically stable in section ‘‘Main result.’’ In section ‘‘Numerical example,’’ numerical example is given. With a known scalar g.0, the closed-loop system in (equation (6)) has a prescribed HN performance index and is stochastically stable, and if it is stochastically stable under zero initial condition, the following inequality holds for all nonzero vk 2 l21⁄20, ‘). Finsler’s Lemma: If there exist d, h, and q with proper dimensions and h are symmetric and rank(q)\n, the conditions (1) and (2) given as follows are equalient. Consider the discrete-time MJLSs (equation (1)) with two modes given as follows
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