STABLE INVERSION FOR NONLINEAR NONMINIMUM-PHASE TIME-VARYING SYSTEMS

In this paper, we extend stable inversion to nonlinear time-varying sy stems and study computational issues-the technique is applicable to mi nimum-phase as well as nonminimum-phase systems, The inversion techniq ue is new, even in the linear time-varying case, and relies on partiti oning (the dichotomic split of) the linearized system dynamics into ti me-varying, stable, and unstable, submanifolds. This dichotomic split is used to build time-varying filters which are, in turn, the basis of a contraction used to find a bounded inverse input-state trajectory, Finding the inverse input-state trajectory allows the development of e xact-output tracking controllers. The method is local to the time-vary ing trajectory and requires that the internal dynamics vary slowly; ho wever, the method represents a significant advance relative to present ly available tracking controllers. Present techniques are restricted t o time-invariant nonlinear systems and, in the general case, track onl y asymptotically.