Finite-time Stability and Stabilization of Markovian Jump Linear Systems Subject to Incomplete Transition Descriptions

• Published in: International journal of control, automation, and systems Vol. 19; no. 9; pp. 2999 - 3012
• Main Authors: Bai, Yuzhu, Sun, Hui-Jie, Wu, Ai-Guo
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.09.2021; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Control; Descriptions; Discrete time systems; Engineering; Feedback control; Linear matrix inequalities; Linear systems; Mathematical analysis; Mechatronics; Regular Papers; Robotics; Stability analysis; State feedback; Time domain analysis; Transition probabilities; 제어계측공학; Finite-time stability; finite-time stabilization; incomplete transition descriptions; Markovian jump linear system
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-020-0505-7

In this paper, the problems of finite-time stability analysis and finite-time stabilization are investigated for Markovian jump linear systems with incomplete transition descriptions. Two sufficient conditions are proposed to guarantee that the system states do not exceed a certain threshold in mean-square sense during a specified time interval for the continuous-time Markovian jump linear systems with partly unknown transition rates and the discrete-time Markovian jump linear systems with partly unknown transition probabilities, respectively. On the basis of the above results, two state feedback controllers are developed to solve the finite-time stochastic stabilization problems of the considered systems in continuous-time domain and discrete-time domain, respectively. For the sake of computational convenience, all the conditions are cast in the format of linear matrix inequalities (LMIs). The main feature of the proposed methods is that the total number of LMIs is much less than that in some existing results. Thus, the solution of the finite-time controllers is more concise both in theory and in engineering. In the end, the validity of the developed theoretical results are demonstrated by two illustrative examples.