H ∞ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities

Lingchun Li; Guangming Zhang; Meiying Ou; Yujie Wang

Kybernetika (2019)

  • Volume: 55, Issue: 1, page 134-151
  • ISSN: 0023-5954

Abstract

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This paper is devoted to design H ∞ 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.

How to cite

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Li, Lingchun, et al. "$H_\infty $ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities." Kybernetika 55.1 (2019): 134-151. <http://eudml.org/doc/294351>.

@article{Li2019,
abstract = {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.},
author = {Li, Lingchun, Zhang, Guangming, Ou, Meiying, Wang, Yujie},
journal = {Kybernetika},
keywords = {Markov jump systems; time-varying delays; sliding mode control},
language = {eng},
number = {1},
pages = {134-151},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$H_\infty $ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities},
url = {http://eudml.org/doc/294351},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Li, Lingchun
AU - Zhang, Guangming
AU - Ou, Meiying
AU - Wang, Yujie
TI - $H_\infty $ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 1
SP - 134
EP - 151
AB - 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.
LA - eng
KW - Markov jump systems; time-varying delays; sliding mode control
UR - http://eudml.org/doc/294351
ER -

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