Observer-based H∞ control for discrete-time one-sided Lipschitz Markovian jump delayed systems under partially unknown transition probabilities. Issue 13 (September 2020)

• Record Type: Journal Article
• Authors: Ghous, Imran; Lu, Jian; Hussain, Waqas
• Is Part Of: Journal of the Franklin Institute. Volume 357:Issue 13(2020)
• Page Start: 8611
• Page End: 8630
• Publication Date: 2020-09
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2020.06.019
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This paper solves H ∞ controller-based observer synthesis problem for the discrete-time non-linear Markovian jump systems (MJSs) with time-varying delays and disturbances in the existence of partially unknown transition probabilities. The non-linear function considered in this work is assumed to satisfy the one-sided Lipschitz (OSL) condition, which is less conservative as compared to the global Lipschitz condition. Firstly, by virtue of an appropriately chosen Lyapunov-Krasovskii functional and the improved summation inequality, some sufficient inequality-based conditions for the existence of a state feedback controller have been proposed for OSL MJSs such that the overall closed-loop system is stochastically stable (SS). Secondly, an observer-based H ∞ control design problem for the system under consideration has been solved such that the overall error dynamics are SS with disturbance attenuation level γ . The results are formulated in terms of linear matrix inequalities. Finally, a suitable example has been discussed to show the significance of the developed results.