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Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities
Author(s) -
Liu Yangfan,
Ma Yuechao,
Wang Yanning
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3872
Subject(s) - control theory (sociology) , discrete time and continuous time , reachability , sliding mode control , nonlinear system , mathematics , controller (irrigation) , lipschitz continuity , settling time , estimator , computer science , engineering , algorithm , control (management) , control engineering , mathematical analysis , statistics , physics , quantum mechanics , artificial intelligence , agronomy , biology , step response
Summary This paper focuses on the problem of finite‐time H ∞ control for one family of discrete‐time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete‐time close‐loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite‐time boundedness and sliding mode H ∞ finite‐time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.