Semi-global stabilization of linear systems with distributed infinite input delays and actuator saturations

Abstract

This paper addresses the semi-global stabilization problem of linear systems with simultaneous presence of distributed infinite input delays and actuator saturations. Two low gain controllers are proposed, respectively, for two classes of linear systems with both infinite input delays and actuator saturations. It is shown that under our first controller, the semi-global stabilization problem can be solved for the first class of systems where all eigenvalues of the open loop system have no positive real parts. It is also shown that under our second controller, which is much simpler, the semi-global stabilization problem can be solved for the second class of systems where all eigenvalues of the open loop system are zero. Another contribution of this paper is that the bounds for the peak magnitude of the control signals can be explicitly given. Furthermore, our results include relevant results on bounded distributed delays and constant delays as their special cases. Simulation examples are finally provided to illustrate the effectiveness of the proposed controllers.