Transformations of solvents and spectral factors of matrix polynomials, and their applications†
Leang San Shieh, YIH TSONG TSAY · International Journal of Control · 1981
The relationships between solvents and spectral factors of a high-degree matrix polynomial are explored. Various new transformations are developed to convert right (left) solvents into spectral factors and vice versa. The transformation of a right (left) solvent to a left (right) solvent is also established. The newly established algorithms are then applied to determine the spectral factorization of a matrix polynomial for optimal control problems. The developed algebraic theory enhances the capability of the analysis and synthesis of a system described by a high-degree matrix differential equation.