H∞ sliding mode control for Markovian jump systems with randomly occurring uncertainties and repeated scalar nonlinearities via delay-fractioning method. (June 2020)

• Record Type: Journal Article
• Authors: Zhang, Panpan; Hu, Jun; Zhang, Hongxu; Chen, Dongyan
• Is Part Of: ISA transactions. Volume 101(2020)
• Page Start: 10
• Page End: 22
• Publication Date: 2020-06
• Subjects: Sliding mode control -- Markovian jumping parameters -- Repeated scalar nonlinearities -- Randomly occurring uncertainties -- Uncertain occurrence probabilities; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2020.01.032
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: This paper addresses the problem of robust H ∞ sliding mode control (SMC) for discrete delayed Markovian jumping systems subject to randomly occurring uncertainties (ROUs) and repeated scalar nonlinearities (RSNs). Here, a set of mutually independent Bernoulli distributed random variables is introduced to model the phenomenon of the ROUs, where the occurrence probabilities could be uncertain. The purpose of paper is to present an H ∞ SMC strategy via the delay-fractioning approach such that, for the Markovian jumping parameters, time-varying delays, ROUs and RSNs, the mean-square stability of the resulted sliding motion with a prescribed H ∞ performance can be guaranteed. Subsequently, the robust sliding mode controller is synthesized to guarantee that the reachability condition in the discrete-time setting is ensured. Finally, the validity of proposed robust SMC strategy is verified by providing a simulation example. Highlights: The mathematical characterization of uncertain occurrence probabilities is given. The H ∞ SMC problem is studied via the delay-fractioning approach. The effects from MJPs, delays, RSNs and ROUs under uncertain occurrence probabilities are examined.