Finite-Time Stability and Stabilization of Discrete-Time Switching Markov Jump Linear System
- PDF / 342,032 Bytes
- 7 Pages / 612.284 x 810.709 pts Page_size
- 50 Downloads / 169 Views
Finite-Time Stability and Stabilization of Discrete-Time Switching Markov Jump Linear System JIN Yunyun 1 (
),
Ý ),
SONG Yang 1,2∗ (
LIU Yongzhuang 1 (
),
HOU Weiyan 3 (
)
(1. Department of Automation, School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200444, China; 2. Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai 200444, China; 3. School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China)
© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: Switching Markov jump linear system (SMJLS), a special hybrid system, has attracted a lot of studies recently. SMJLS is governed by stochastic and deterministic commutations. This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems. Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided, and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities (LMIs). Finally, numerical examples are given to show the feasibility and effectiveness of the results. Key words: switching Markov jump linear system (SMJLS), finite-time stability, stochastic switching, deterministic switching, minimum dwell time CLC number: TP 273 Document code: A
0 Introduction Switching system has been a research hotspot in recent decades. The analysis and the control of switching system have attracted extensive attention from many researchers[1]. In recent years, many achievements have been made in the study of switching systems, including controllability, reachability, stabilizability control[2-6] , design of switching law[7-9] , and optimal control[10-11] of the system, among which the most important aspects are the stability analysis and stabilization control of the switching system. The main approaches for investigating the stability of switching systems include the minimum dwell-time and average dwell-time. Markov jump linear system (MJLS) is a kind of stochastic hybrid system. MJLS is composed of a set of linear systems, generally known as modes, and the transition between modes is governed by a Markov chain[12] . They are well suited to represent dynamic systems that switch randomly between alternative structures[13] . MJLS has been widely used in network control systems (NCs)[12] , tolerant systems[14] , power systems, and aerospace systems. In the past decade, the Received date: 2020-02-22 Foundation item: the National Natural Science Foundation of China (No. 61573237), the “111 Project” (No. D18003), and the Program of China Scholarship Council (No. 201906895021) ∗E-mail: y [email protected]
stability research of MJLS mainly focused on stochastic stability[15] , mean square stability (MSS)[16] , δmoment stability[17] , exponential almost sure stability (EASS)[18] , etc. In the study of system stability, attention should be paid to the
Data Loading...
