Rendering a Prescribed Subset Invariant for Polynomial Systems by Dynamic State-Feedback Compensator

Abstract: This paper derives a sufficient condition for the existence of a dynamic state-feedback compensator, for a polynomial system, such that a prescribed subset defined by an algebraic inequality is invariant for the resulting closed-loop system. Moreover, we present an algorithm for exactly computing such a compensator. The algorithm consists of finitely-many arithmetic operations of polynomials.