Coupled polynomial equations for LQ control synthesis and an algorithm for solution

Abstract

The polynomial equation approach can be used to solve a variety of important control problems. The approach leads to the requirement to solve linear polynomial equations. We present a new algorithm for the numerical solution of a general coupled pair of linear polynomial equations. The algorithm is based upon the method of polynomial reductions. Theoretically, solving the coupled equations together enhances the numerical robustness of the equation solution. The algorithm finds a specific and unique minimal degree solution of the equations. The general couple of equations studied is representative of a number of problems in linear control theory, and the minimal degree solution usually corresponds to an optimizing solution of the control problem