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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.

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