Finite-Time H ∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities

• Published in: Entropy (Basel, Switzerland) Vol. 26; no. 4; p. 292
• Main Authors: Guo, Xinye, Li, Yan, Liu, Xikui
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 27.03.2024
• Subjects: Closed loops; Control systems; Discrete time systems; Euclidean space; Feedback control; finite-time control; H-infinity control; H∞ control; Linear matrix inequalities; Markovian jump systems; Mathematical analysis; Mutation; Neural networks; partly unknown transition probabilities; Probability; State feedback; Transition probabilities; discrete-time systems; Markovian jump systems; H∞ control; finite-time control; partly unknown transition probabilities
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e26040292

This paper concentrates on the finite-time H∞ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) H∞ state feedback controller and an SFT H∞ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov-Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT H∞ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.