Controlled Invariant Polyhedral Sets for Constrained Discrete-Time Descriptor Systems

Abstract : This paper addresses the problem of constructing controlled invariant polyhedral sets for linear discrete-time descriptor systems subject to state and control constraints and persistent disturbances. Regardless the large number of contributions on set invariance for linear systems in the standard form, there are few works dealing with set invariance properties in the case of descriptor systems. Here, assuming regularity and causality of the descriptor system, the state equations are written in such way that standard algorithms can be directly applied. Moreover, state and control constraints can be enforced through a piecewise linear delayed state feedback. A numerical example is presented to illustrate these ideas.