Fixed Structure Controller Synthesis Using Groebner Bases and Sign-Definite Decomposition*
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This paper presents a new method for computing stabilizing fixed structure/order controllers using Groebner bases and sign-definite decomposition. An application of Routh-Hurwitz stability condition results in a system of polynomial inequalities that must be satisfied by the parameters of any stabilizing controller. Using positive slack variables, the system of polynomial inequalities can be converted to a system of polynomial equations. With the aid of Groebner bases and elimination theory, an equivalent system of polynomial equations can be obtained which simplifies the construction of the set of stabilizing controllers using the sing-definite decomposition. The results of this approach are illustrated by examples provided. © 2011 IFAC.
author list (cited authors)
Mohsenizadeh, N., Darbha, S., & Bhattacharyya, S. P.