$H_\infty $ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities

Li, Lingchun ; Zhang, Guangming ; Ou, Meiying ; Wang, Yujie

Kybernetika, Tome 55 (2019) no. 1, pp. 134-151

Abstract (VO)

This paper is devoted to design $H_\infty$ sliding mode controller for continuous-time Markov jump systems with interval time-varying delays and general transition probabilities. An integral sliding surface is constructed and its reachability is guaranteed via a sliding mode control law. Meanwhile, a linearisation strategy is applied to treat the nonlinearity induced by general transition probabilities. Using a separation method based on Finsler lemma to eliminate the coupling among Lyapunov variables and controller parameters, sufficient conditions for asymptotically stochastic stability of sliding mode dynamics are formulated in terms of linear matrix inequalities. Finally, a single-link robot arm system is simulated to demonstrate the effectiveness of the proposed method.

Détail

DOI : 10.14736/kyb-2019-1-0134

Classification : 93D09, 93D15, 93E03
Keywords: Markov jump systems; time-varying delays; sliding mode control

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