an:05232242
Zbl 1141.93043
Aguirre, Baltazar; Su??rez, Rodolfo
Algebraic test for the Hurwitz stability of a given segment of polynomials
EN
Bol. Soc. Mat. Mex., III. Ser. 12, No. 2, 261-275 (2006).
00194770
2006
j
93D09 34D99 93C05
Hurwitz stable polynomials; segments of polynomials; minimum left extreme; matrix inequalities
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.