FACTORIZATION OF MATRIX POLYNOMIALS WITH CONSTRAINTS ON DEGREES

A direct algebraic relationship between the spectral and time-domain m ethods is found for the design of H-infinity-optimal controllers. In p articular, the existence of a solution of the adjoint Lur'e-Riccati eq uation is equivalent to the existence of the factorization of a polyno mial matrix which is equal to an algebraic sum of the squares of the t ransfer functions of an open system in the case where the matrix invol ves additional constraints imposed on the degree of a multiplier The c oncept of a polynomial Riccati equation is evolved. Comprehensive feat ures of the convergence of the algorithm designed by Davis, Callier, a nd Kwakernaak for the sequential reduction of multipliers are set out.