Finite-Time Control of Markov Jump Lur'e Systems With Singular Perturbations
Jun Cheng, Ju H. Park, Zheng‐Guang Wu
Abstract
This paper investigates the asynchronous controller design issue for Markov jump Lur'e systems with singular perturbations within a fixed time interval. For broader practical applications, the variation of system modes is regulated by a switched nonhomogeneous Markov process that corresponded to both lower-level nonhomogeneous stochastic jumping and higher-level deterministic switching. By resorting to the hidden nonhomogeneous-Markov model, an asynchronous control law that relies on the detected mode information is proposed. In light of the mode-dependent average dwell time strategy and mode-dependent stochastic system theory, the singularly perturbed parameter-independent conditions are attained to ensure the stochastic finite-time boundedness of the resulting systems. With respect to a linear matrix inequality optimization problem, a solution to the maximum singular perturbation parameter is obtained. Finally, the feasibility and applicability of the devised theoretical results are verified by simulation examples.