Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates

• Published in: Applied Mathematical Modelling Vol. 53; pp. 49 - 70
• Main Authors: Ma, Yuechao, Jia, Xiaorui, Liu, Deyou
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.01.2018; Elsevier BV
• Subjects: Actuator saturation; Controllers; Convexity; Discrete time systems; Discrete-time singular system; Dissipation; Feedback control; Finite-time dissipative control; Jumping; Linear matrix inequalities; Linear matrix inequality; Markov analysis; Markov processes; Mathematical analysis; Matrix methods; Optimization; Partly unknown transition rates; Saturation; State feedback; Stochastic models; Finite-time dissipative control; Linear matrix inequality; Actuator saturation; Discrete-time singular system; Partly unknown transition rates
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2017.07.035

•A new control problem for discrete singular Markov system is investigated.•Lyapunov function method, LMI technique and convex optimization are used.•Both actuator saturation and partly unknown transition rates are considered.•The derived conditions are less conservative have wider application range. In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and partly unknown transition rates. By constructing a proper Lyapunov–Krasonski functional and the method of linear matrix inequalities (LMIs), sufficient conditions that ensure the systems singular stochastic finite-time stability and singular stochastic finite-time dissipative are obtained. Then, the state feedback controllers are designed, and in order to get the optimal values of the dissipative level, the results are extended to LMI convex optimization problems. Finally, numerical examples are given to illustrate the validity of the proposed methods.