In this paper, we deal with two problems of input-affine polynomial dynamical systems. One aims to obtain a state feedback controller such that a prescribed algebraic set is invariant for the resulting closed-loop system. The other aims to obtain a state feedback controller such that the resulting closed-loop system has a prescribed vector field on a given algebraic set. It is shown that the two problems can be represented by a particular inclusion of polynomials, and the inclusion can be solved. As a result, all the state feedback controllers required in the problems can be exactly represented by using free polynomial parameters.
In this paper, we deal with two problems of static output feedback for input-affine polynomial dynamical systems. One is to design a static output-feedback controller so as to render a prescribed algebraic set invariant for the resulting closed-loop system. The other is to design a static outputfeedback controller so as to realize a prescribed vector field on a prescribed algebraic set. It is shown that the two problems can be represented by a particular inclusion of polynomials, and the inclusion can be solved. As a result, all the static output-feedback controllers required in the problems can be exactly represented by using free polynomial parameters.
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