Nonlinear noninteracting control with stability: a high gain control approach

The problem of designing a controller to render a class of nonlinear systems simultaneously noninteractive with asymptotically stable fixed modes is addressed. It is shown that for a nonlinear system with unstable fixed dynamics (nonminimum phase system) where there exists no dynamic state feedback which could render the closed-loop system noninteractive and stable, a high-gain dynamic control strategy exists which achieves noninteraction with stability. The use of this control strategy introduces a two-time scale in the closed-loop system dynamics. By utilizing the concept of integral manifold, an exact reduced order model of the full order system is obtained. Using this, it is possible to design a dynamic state feedback controller which would simultaneously result in asymptotically stable fixed dynamics and a noninteracting input/output map