A Computational Method for Determining Strong Stabilizability of n-D Systems

Abstract

This paper describes an algorithm for the following problem: given two multivariate complex or real polynomials f and g , decide whether there exist complex or real polynomials h and k such that both k and fh+gk have no zero in the unit polydisc. This problem, known as strong stabilizability, is fundamental in control theory, with important applications in designing stable feedback systems with a stable compensator. Our algorithm for solving the problem is formulated based on the cylindrical algebraic decomposition(cad) of an algebraic variety. While recent applications of cad to systems and control have been focused on those problems which have a quantifier elimination formulation, our method is novel in that it explicitly computes some topological properties of an algebraic variety based on the cad to solve the problem for which a quantifier elimination formulation is not readily available.