Observer-based H_∞ control for uncertain one-sided Lipschitz Markovian jump-delayed systems with partially unknown transition rates

Abstract

This paper addresses the observer-based control design for uncertain one-sided Lipschitz Markovian jump-delayed systems. By constructing the Lyapunov functional of the closed-loop augmented system, combining with the one-sided Lipschitz condition and quadratically inner-bounded condition, it is derived that the closed-loop augmented system is stochastic stable with an [Formula: see text] performance level [Formula: see text]. With the help of some special derivations, bilinear matrix inequalities are successfully transformed into a group of linear matrix inequalities. The robust controller and observer gains are solved by linear matrix inequality (LMI) toolbox in MATLAB.