Robust and non-fragile H∞ control for a class of uncertain hybrid linear systems with Markovian jumping parameters

This paper describes the synthesis of robust and non-fragile H_∞ state feedback controllers for a class of uncertain hybrid linear systems with time delay, Markovian jumping parameters and state multiplicative noise. Under the assumptions of complete access to the norm-bounds of the system uncertainties and controller gain variations, sufficient conditions on the existence of a robust stochastic stability and r-disturbance attenuation H_∞ property are presented. Also, using some change of variables and Schur complements, the obtained sufficient conditions can be rewritten as a set of coupled linear matrix inequalities form, through which a robust and non-fragile controller can be constructed easily.