Nonlinear H 1 Optimization : A Causal Power Series Approach

In this paper, using a power series methodology we describe a design procedure applicable to analytic nonlinear plants. Our technique is a generalization of the linear H theory. In contrast to previous work on this topic ([3], [14], [15]), we now are able to explicitly incorporate a causality constraint into the theory. In fact, we show that it is possible to reduce a causal optimal design problem (for nonlinear systems) to a classical interpolation problem solvable by the commutant lifting theorem [25], [12]. This paper has appeared in SIAM J. Control and Optimization 33 (1995), pp. 185{207. 1980 Mathematics Subject Classi cations (1985 Revision). Primary 47A20, Secondary 47A99, 93B35, 93C05.