Nonlinear H-infinity control around periodic orbits

In this paper, we study the nonlinear H-infinity control of systems with periodic orbits. We develop the notion of an induced L-2 gain (so-called nonlinear H-infinity norm) for systems where the no-disturbance behavior of the system is a periodic orbit and provide conditions under which the induced L, gain of the system (around the orbit) can be made less than a specified value by state feedback. This work is a natural extension of results on nonlinear H-infinity control of nonlinear systems in a neighborhood of a stable equilibrium point to the periodic orbit case. Synthesis of a nonlinear H-infinity state feedback controller is facilitated by the use of transverse coordinates and, in particular, the transverse linearization of the system. (C) 1997 Published by Elsevier Science B.V.