In this paper, preliminary simulation studies about signal perfect reconstruction, around wireless transmission with non-equal transmit/receive antennas, was presented. The polynomial-matrix equation, in particular Smith factorization based on polynomial S-inverse, has been taking into account .
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Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.
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Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method of computing of the set of positive solutions to a polynomial diophatine equation based on extreme points and extreme directions is proposed. The effectiveness of the method is demonstrated on a numerical example.
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