Observer-based H∞ control for discrete-time one-sided Lipschitz Markovian jump delayed systems under partially unknown transition probabilities

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.