Lie Derivative Inclusion with Polynomial Output Feedback

Abstract

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.

Attracting and Natural Invariant Varieties for Polynomial Vector Fields and Control Systems

“…The theory has been generalized to nonlinear systems by Isidori [10] and several other authors. Recently, some progress has been made in the area of nonlinear polynomial systems; see [15][16][17]21], and Yuno and Ohtsuka [19,20], where it is shown that methods from symbolic computation can be used to test the conditions for controlled invariance of varieties constructively. The purpose of the present work, which is in part based on the doctoral dissertations [11,17] by two authors of the present manuscript, is twofold.…”