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Algebraic test for the Hurwitz stability of a given segment of polynomials. (English) Zbl 1141.93043
Summary: For the robust stability analysis of a linear system, due to the nonconvexity of the set of Hurwitz stable polynomials, it is important to have available computational methods to verify the stability of a convex combination of polynomials. In this paper, given two Hurwitz stable polynomials \(p_0\) and \(p_1\), a simple algebraic test (a matrix inequality) for the stability of the segment of polynomials determined by \(p_0\) and \(p_1\) is proposed. Based on this result the problem of estimating of the minimum left extreme is addressed.

93D09 Robust stability
34D99 Stability theory for ordinary differential equations
93C05 Linear systems in control theory