On Finite-Time Stochastic Stability and Stabilization of Markovian Jump Systems Subject to Partial Information on Transition Probabilities

• Published in: Circuits, systems, and signal processing Vol. 31; no. 6; pp. 1973 - 1983
• Main Authors: Zuo, Zhiqiang, Li, Hongchao, Liu, Yi, Wang, Yijing
• Format: Journal Article
• Language: English
• Published: Boston SP Birkhäuser Verlag Boston 01.12.2012; Springer Nature B.V
• Subjects: Circuits; Circuits and Systems; Criteria; Electrical Engineering; Electronics and Microelectronics; Engineering; Instrumentation; Markov analysis; Mathematical models; Mean square values; Signal,Image and Speech Processing; Stability; Stabilization; Stochastic models; Stochasticity; Systems stability; Transition probabilities; Finite-time stochastic stability; Markovian jump systems; Partial information on transition probabilities
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-012-9420-3

The problems of finite-time stochastic stability and stabilization for a class of linear Markovian jump systems subject to partial information on transition probabilities are considered in this paper. By introducing the concept of finite-time stochastic stability for linear Markovian jump systems, a new method is proposed to ensure that the state trajectory remains in a bounded region of the state space in mean square sense over a pre-specified finite-time interval. Based on this stability result, the finite-time stochastic stabilization criterion is then given. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed method.