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Stability analysis and saturation control for nonlinear positive Markovian jump systems with randomly occurring actuator faults
Author(s) -
Zhang Junfeng,
Yang Haoyue,
Raïssi Tarek
Publication year - 2020
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.5042
Subject(s) - control theory (sociology) , nonlinear system , actuator , lyapunov function , markov process , saturation (graph theory) , mathematics , stability (learning theory) , controller (irrigation) , computer science , control (management) , physics , statistics , quantum mechanics , artificial intelligence , combinatorics , machine learning , agronomy , biology
Summary This article investigates the stability analysis and control design of a class of nonlinear positive Markovian jump systems with randomly occurring actuator faults and saturation. It is assumed that the actuator faults of each subsystem are varying and governed by a Markovian process. The nonlinear term is located in a sector. First, sufficient conditions for stochastic stability of the underlying systems are established using a stochastic copositive Lyapunov function. Then, a family of reliable L 1 ‐gain controller is proposed for nonlinear positive Markovian jump systems with actuator faults and saturation in terms of a matrix decomposition technique. Under the designed controllers, the closed‐loop systems are positive and stochastically stable with an L 1 ‐gain performance. An optimization method is presented to estimate the maximum domain of attraction. Furthermore, the obtained results are developed for general Markovian jump systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed techniques.