Case studies on the control of input-constrained linear plants via output feedback containing an internal deadzone loop

In this chapter we address several case studies using LMI optimization methods 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. © 2007 Springer.