Passivity approach to feedback connection stability for discrete-time descriptor systems

Abstract

The linear matrix inequality (LMI)-based passivity approach to studying both input-output and internal stability problems for feedback connections of discrete-time linear descriptor systems with passive nonlinearities is developed. We show that, under a mild condition, a set of LMIs is equivalent to the strictly positive realness of the linear descriptor systems, and is strong enough to guarantee both the finite gain l/sub 2/-stability and asymptotic hyperstability of the feedback connection.