Reliable finite-time H∞ control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay

• Published in: International journal of systems science Vol. 48; no. 11; pp. 2249 - 2261
• Main Authors: Ma, Yue-Chao, Liu, Yang-Fan, Chen, Hui
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 18.08.2017; Taylor & Francis Ltd
• Subjects: bounded transition probabilities; Controllers; decoupling; Decoupling method; Delay; Feedback control; finite-time boundedness; Infinity; Linear matrix inequalities; linear matrix inequalities (LMIs); Markov analysis; Markov processes; Markovian jump systems; Mathematical analysis; Mathematical models; Matrix methods; Probability theory; Randomness; Reliable singular stochastic H; state estimation; Time lag; Transition probabilities
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2017.1318972

This paper investigates the problem of reliable finite-time H ∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H ∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov-Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach.