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<html>H<sub>∞</sub> sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities</html>

Lingchun Li, Guangming Zhang, Meiying Ou, Yujie Wang

Year
2019
Citations
2

Abstract

summary: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.

Keywords

Interval (graph theory)MathematicsMarkov chainJumpControl theory (sociology)Discrete mathematicsApplied mathematicsControl (management)Computer scienceCombinatorics

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