A sufficient condition for the stability of interval matrix polynomials

The root location of sets of scalar polynomials whose coefficients are confined to intervals and the associated extension to eigenvalues of sets of constant matrices whose coefficients are contained in intervals are reviewed. A central result for complex scalar interval polynomials is a theorem developed by V.L. Kharatonov (1978), which states that each member of a set of such polynomials is stable if and only if eight special polynomials from the set are stable. The case of interval matrix polynomials is examined, and a Kharitonov-like result for their strong stability is provided. This in turn yields a sufficient condition for stability of a set of interval matrix polynomials.<
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