A class of weak Kharitonov regions for robust stability of linear uncertain systems

Kharitonov's theorems are generalized to the problem of so-called weak Kharitonov regions for robust stability of linear uncertain systems. Given a polytope of (characteristic) polynomials P and a stability region D in the complex plane, P is called D-stable if the zeros of every polynomial in P are contained in D. It is of interest to know whether the D-stability of the vertices of P implies the D-stability of P. A simple approach is developed which unifies and generalizes many known results on this problem.<
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