Abstract
The linear combination of polynomial matrices is considered as an entity, the matrix polynomial equation. Necessary and sufficient conditions for the existence of a solution are considered, and the general solution is studied. It is shown that a number of computational algorithms such as the Euclidean algorithm, partial fractions’ problem, the spectral factorization problem, may be considered using the concept of matrix polynomial equations and, as a result, methods of solution are derived that are computationally simpler than existing methods of solution. Further, the concept and methods of polynomial equations are used to analyze some of the problems in multivariable control such as the system invariants under state feedback, conditions for exact model matching and problem of decoupling.
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