Output feedback control for a class of switching discrete-time linear systems

This paper is concerned with the output feedback control of switching linear systems without knowledge of the current switching mode. An observer-based control scheme is proposed that is based on the cascade of a Luenberger observer to estimate the continuous state, a mode estimator, and a controller fed with the estimates of both continuous state variables and mode. Conditions for the stability of such a control scheme are presented in both a noise-free setting and a noisy one because of bounded disturbances. Linear matrix inequalities are used to express such conditions with a reduced conservativeness as compared with the results available in the current literature. The effectiveness of the proposed approach is shown by means of simulations.