Input-output stability of a broad class of linear time-invariant multivariable systems

Abstract

The input-output stability of closed loop control systems, which are not necessarily open loop stable, is considered. The type of stability considered is very broad, and encompasses bounded-input-bounded-output stability. Both continuous-time and discrete-time systems are considered. It is shown that the Desoer-Wu condition [2] is both necessary and sufficient for a large class of closed loop systems to be stable. The criterion is applicable to multivariable systems as well as to single-input-single-output systems.