Practical stability and stabilization of linear systems

Abstract

In this paper practical stability and stabilization of linear continuous systems, modeled in state space and subject to state norm constraints, are considered. First, we provide condition for practical stability using the norm of the transition matrix. Then we give conditions guaranteeing the existence and the synthesis of a state feedback controller and a static output feedback controller which practically stabilize the system with respect to state norm constraints. Conditions guaranteeing the design of a controller which ensures both practical and asymptotic stability are then proposed. The latter conditions relative to simultaneous practical and asymptotic stability are extended to the case of uncertain systems.