Mixed L_1/H-infinity control for uncertain linear singular systems

The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and ＊-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.