Linear systems with input nonlinearities: Global stabilization by scheduling a family ofH∞‐type controllers

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Abstract
A new global stabilization algorithm is presented for linear systems that have (A,B) stabilizable, the eigenvalues ofAin 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 ofH∞‐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.

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