LINEAR-SYSTEMS WITH INPUT NONLINEARITIES - GLOBAL STABILIZATION BY SCHEDULING A FAMILY OF H-INFINITY-TYPE CONTROLLERS

A new global stabilization algorithm is presented for linear systems that have (A, B) stabilizable, the eigenvalues of A in the closed left-half plane, but where the controls pass through nonlinearities of a general type. This algorithm is based on a semi-global stabilization solution for the same class of systems. The global solution is constructed by dynamically scheduling the adjustable parameter of the semi-global solution according to the size of the state. The semi-global solution is a family of linear control laws generated by a family of H-infinity-type algebraic Riccati equations. We show that the closed-loop state feedback system has the property that additive disturbances which converge exponentially to zero cannot produce unbounded states. This fact is used to show that, under a linear detectability assumption, the state feedback results are recovered when the solution is implemented via a standard linear-based observer.