NONLINEAR H-INFINITY CONTROL AROUND PERIODIC-ORBITS

In this paper, we study the nonlinear H-infinity control of systems wi th periodic orbits. We develop the notion of an induced L-2 gain (so-c alled nonlinear H-infinity norm) for systems where the no-disturbance behavior of the system is a periodic orbit and provide conditions unde r which the induced L, gain of the system (around the orbit) can be ma de less than a specified value by state feedback. This work is a natur al extension of results on nonlinear H-infinity control of nonlinear s ystems in a neighborhood of a stable equilibrium point to the periodic orbit case. Synthesis of a nonlinear H-infinity state feedback contro ller is facilitated by the use of transverse coordinates and, in parti cular, the transverse linearization of the system. (C) 1997 Published by Elsevier Science B.V.