Robust H∞ sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities

• Published in: Systems & control letters Vol. 62; no. 12; pp. 1114 - 1124
• Main Authors: Zhang, Hui, Wang, Junmin, Shi, Yang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2013
• Subjects: [formula omitted] control; Markovian jump systems; Partially known transition probabilities; Sliding-mode control (SMC); Sliding-mode control (SMC); Markovian jump systems; Partially known transition probabilities; H∞ control
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2013.09.006

In this paper, we exploit the robust H∞ sliding-mode controller design problem for discrete-time Markovian jump linear systems which are subject to intermittent observations and partially known transition probabilities. The intermittent measurements are described by a Bernoulli process and the phenomenon of the partially known transition probabilities is modeled by employing the polytopic uncertainties. A robust mode-dependent estimator is firstly designed to estimate the system states with the intermittent observations. In order to achieve a good transient performance, the circular region is used to constrain the eigenvalues of the filtering error system’s system matrix. With the estimated state vector and the derived observer gain, we propose the design method for the sliding-mode controller with a disturbance predictor and analyze the stability of the closed-loop system. Two numerical examples are provided to illustrate the advantages and the efficacy of the proposed method when simultaneously considering the intermittent observations, the system uncertainty, and the external disturbance.