Feedback Control of Discrete Linear Switching Systems with Bounded State and Control Input in the Presence of Disturbances

The main contribution of this paper is to present some stability synthesis results for a subclass of hybrid systems, which is the discrete-time linear switching systems whose dynamics contain reset functions and are determined by exogenous and uncontrollable events. In the presence of additive bounded disturbances, with state and control input constraints, the linear state feedback controller design that can stabilize the system is investigated in the sense of input-to-state stability (ISS). The concept of controlled D-invariance is introduced for this class of hybrid systems, and a necessary and sufficient condition to test the controlled D-invariance of a hybrid region is given. After this, a procedure for the computation of the feedback matrices, which can stabilize the disturbed linear switching systems and also satisfy the state and control input constraints, is proposed. Finally, a numerical example made up of two subsystems is given to show the applicability of the technique.