Control of saturated linear plants via output feedback containing an internal deadzone loop

In this paper we address a LMI-based optimization method for designing output feedback control laws to achieve regional performance and stability of linear control systems with input saturation. Algorithms are developed for minimizing the upper bound on the regional L₂ gain for exogenous inputs with L₂ norm bounded by a given value, and for minimizing this upper bound with a guaranteed reachable set or domain of attraction. Based on the structure of the optimization problems, using the projection lemma, the output feedback controller synthesis is cast as a convex optimization over linear matrix inequalities. The problems are studied in a general setting where the only requirement on the linear plant is detectability and stabilizability