Parameter Space Stability Analysis Revisited : Kharitonov-Type Theorems and Their Application

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1. Studies were made on conditions for a polytope of matrices to belong to P- (M-) matrices, matrix classes that have close ties to the stability analysis of control systems. Necessary and sufficient conditions for some specific situations and sufficient conditions for a general case are derived.2. An answer is given to the problem on characterization of the class of systems that maintain stability under additive parameter perturbations. The employed method is the Lyapunov's second method. Some illustrative examples are worked out.3. Stability is studied for interval polynomials with vanishing extreme coefficients. It is found that Kharitonov's theorem almost remains valid even in this situation.4. Aperiodicity and periodicity of interval polynomials are investigated and exact conditions for them are given. It is claimed that we have only to check two extreme polynomials.