Abstract
This paper investigates the slow state variable feedback control issue for a group of singularly perturbed Markov jump systems with time-varying state delay in the discrete-time domain. The primary goal of this paper is to propose a slow state controller design approach that ensures the closed-loop dynamics attain stochastic stability with an H∞ performance. First, the time-varying delay is introduced into system state and Markov jump chain is employed to depict system topological change. Secondly, by resorting to the Lyapunov functional theory and matrix analysis method, several necessary criteria are provided to guarantee the desired control performance. The derived conditions rely not only on the size of time-varying state delay and the upper bound of the singular perturbation parameter, but also on the order of the generated Markov jump mode sequence. Based on the established conditions, the gains of the desired slow state controller are obtained by means of the feasibility of a set of linear matrix inequalities. Eventually, a numerical simulation and a tunnel diode circuit model are presented to demonstrate the efficiency of the proposed technique.
Published Version
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