Finite-Time Observer-Based Sliding-Mode Control for Markovian Jump Systems With Switching Chain: Average Dwell-Time Method

• Published in: IEEE transactions on cybernetics Vol. 53; no. 1; pp. 248 - 261
• Main Authors: Zhang, Panpan, Kao, Yonggui, Hu, Jun, Niu, Ben, Xia, Hongwei, Wang, Changhong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Average dwell-time method; Chains; Control systems design; Delays; Dwell time; Estimation; finite-time boundedness; Linear matrix inequalities; Markov chains; Markovian jump systems (MJSs); Observers; Random variables; Robust control; Sliding mode control; sliding-mode observer; Switches; Switching; switching chain
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2021.3093162

In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.