Saturated linear quadratic regulation of uncertain linear systems: stability region estimation and controller design

This paper considers the problems of estimating the stability region (domain of attraction) and controller design for uncertain linear continuous-time systems with input saturation when linear quadratic (LQ) optimal controller is used. By exploiting the structure of the LQ controller and the property of saturation functions, it is established that the estimation of stability region can be obtained by solving linear matrix inequality (LMI) problems. Moreover, an iterative LMI (ILMI) algorithm is presented to design an LQ controller such that the largest estimated stability region can be obtained. Two examples are given to compare our results with existing ones.