Stochastic Stabilization of Discrete-Time Markov Jump Systems with Generalized Delay and Deficient Transition Rates

• Published in: Circuits, systems, and signal processing Vol. 36; no. 6; pp. 2521 - 2541
• Main Authors: Dzung, Nguyen Trung, Hien, Le Van
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-06-2017; Springer Nature B.V
• Subjects: Accessibility; Circuits; Circuits and Systems; Delay; Design; Discrete time systems; Electrical Engineering; Electronics and Microelectronics; Engineering; Inequalities; Instrumentation; Markov analysis; Markov processes; Short Paper; Signal,Image and Speech Processing; Stabilization; Stochastic models; Time delay; Jesen-based inequalities; Stochastic stability; Markov jump systems; Mode-dependent delay
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-016-0410-8

In this paper, the problem of mode-dependent state feedback controller design is studied for discrete-time Markov jump systems with generalized delay and deficient transition rates. The time delay under consideration is subject to mode-dependent and time-varying, and the transition probabilities of the jumping process are assumed to be partially accessible. By utilizing some novel summation inequalities, and by constructing an improved Lyapunov–Krasovskii functional which comprises a mode-dependent quadratic functional and some single, double and triple summation terms, delay-dependent stabilization conditions are derived in terms of tractable linear matrix inequalities. Two numerical examples are given to illustrate the effectiveness of the proposed conditions.