Disturbance Rejection for Markov Jump Systems with Partly Unknown Transition Probabilities and Saturation

• Published in: Circuits, systems, and signal processing Vol. 32; no. 6; pp. 2783 - 2797
• Main Authors: Liu, Yanqing, Liu, Fei
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2013; Springer Nature B.V
• Subjects: Circuits and Systems; Disturbances; Dynamical systems; Electrical Engineering; Electronics and Microelectronics; Engineering; Instrumentation; Markov processes; Optimization; Probability; Probability theory; Randomness; Rejection; Saturation; Signal,Image and Speech Processing; Transition probabilities; Tolerance analysis; Disturbance rejection; Discrete Markov jump system; Partly unknown transition probabilities; Saturation
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-013-9593-4

This paper mainly investigates the disturbance rejection problem of Markov jump systems with bounded disturbance and saturation, in the case that only part of the transition probabilities are known in the discrete-time domain. The mode-dependent state feedback controller is designed to ensure that the resulting closed-loop system is stochastically stable and satisfies the optimal disturbance rejective index, meanwhile, the state of the system is to remain in an expected small region including origin in terms of disturbances. Specifically, the stochastically stable conditions are formulated by parameter-dependent Lyaponuv methodology and further established as linear matrix inequalities (LMIs). Sweeping the auxiliary parameters in the domain of definition, the global optimal disturbance rejective index is obtained. Finally, tolerance capability is further analyzed to evaluate the disturbance rejection level. Two numerical examples, a common linear system and a Markov jump system with completely known and partly unknown transition probabilities, are presented to illustrate the potential of the results, respectively.