Stabilization of unsymmetrical saturated control systems

Abstract

This chapter deals with the regulator problem for discrete-time and continuous-time linear systems with asymmetric saturation on the control. The main contribution of this work is to extend the available results for symmetrical saturation to the case of unsymmetrical saturation. The results are expressed in term of LMIs. New less conservative results on saturation are obtained. Symmetrization of the problem is obtained via some change of variables. First, an approach where the regularity of the system matrix is needed is presented. Second, this assumption is removed leading to an improved approach based on the same symmetrization techniques. An example is presented, in each case, to illustrate the obtained results.