Optimal l disturbance attenuation and global stabilization of linear systems with bounded control

Abstract

This papers addresses the problem of globally minimizing the worst-case response to persistent l∞ bounded disturbances in linear systems with bounded control action. The main result of the paper shows that in the state-feedback case the best performance among all stabilizing controllers (possibly discontinuous, nonlinear time varying) is achieved by a memoryless, continuous, feedback control law. In the case of open-loop stable plants the proposed control law renders the system globally stable and provides the best possible l∞ attenuation in every neighbourhood of the origin. In the case of open-loop unstable plants this law optimizes performance in the region where a finite l∞ gain can be achieved. Copyright © 1999 John Wiley & Sons, Ltd.