Fuzzy-Model-Based Control for Singularly Perturbed Systems With Nonhomogeneous Markov Switching: A Dropout Compensation Strategy
Jun Cheng, Wentao Huang, Hak‐Keung Lam, Jinde Cao, Yinghui Zhang
Abstract
This article addresses the asynchronous control for singularly perturbed systems with nonhomogeneous Markov switching approximated by T–S fuzzy models. The transition probabilities of the nonhomogeneous Markov process are supposed to be time-varying and distinguished by of a polytopic set. As distinct from some reported works, to abate the effect of missing packets in unreliable communication network, a novel dropout compensation strategy is constructed, where the packet arriving rate is assumed to be uncertain. Meanwhile, to describe the asynchronizations of the dropout compensation strategy and the controller, the hidden Markov models are absorbed. By resorting to the fuzzy-rule-dependent and the parameter-dependent Lyapunov–Krasovskii functional, novel sufficient conditions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance are formulated and the fuzzy-based asynchronous controller gains are realized. Finally, to testify the efficiency and applicability of the proposed results, a numerical example and practical tunnel diode circuit system are provided.