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

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