COUPLED POLYNOMIAL EQUATIONS FOR LQ CONTROL SYNTHESIS AND AN ALGORITHM FOR SOLUTION

The polynomial equation approach can be used to solve a variety of imp ortant control problems. The approach leads to the requirement to solv e linear polynomial equations. We present a new algorithm for the nume rical solution of a general coupled pair of linear polynomial equation s. The algorithm is based upon the method of polynomial reductions. Th eoretically, solving the coupled equations together enhances the numer ical robustness of the equation solution. The algorithm finds a specif ic and unique minimal degree solution of the equations. The general co uple of equations studied is representative of a number of problems in linear control theory, and the minimal degree solution usually corres ponds to an optimizing solution of the control problem.