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Robust stability of convex combination of two fractional degree characteristic polynomials

Busłowicz M.

Acta Mechanica et Automatica

2008

Vol. 2, no. 2

5-10

The paper considers the problem of robust stability of convex combination of two fractional degree characteristic polynomials. This problem is equivalent to the problem of robust stability of linear continuous-time fractional systems with characteristic polynomial linearly dependent on one uncertain parameter. Frequency domain methods for robust stability analysis of such a combination are given. The methods proposed are based on the Zero Exclusion Condition known from the theory of robust stability of families of natural degree polynomials. The considerations are illustrated by numerical example.

Stability of the convex combination of polynomials

Góra M.

Control and Cybernetics

2007

Vol. 36, no 2

425-442

In this paper, we consider the convex combination of polynomials. We provide a necessary and sufficient condition for Hurwitz stability of the convex combination of m real polynomials (m ≥ 3) whose degrees may be different and both necessary, and necessary and sufficient conditions for Hurwitz and Schur stability of the convex combination of two complex polynomials. We show also that the convex combination of two polynomials whose degrees are respectively odd and even, is never Schur stable. We give a few examples completing the results.

Criterions for the stability of the convex combination of polynomials

Zalot E.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

2006

T. 10, z. 1

87-95

Necessary and sufficient conditions for Hurwitz (resp. Schur) stability of convex combination of two complex polynomials are introduced in the paper. The conditions are more general than those given in [2] and supplement work [3].

W pracy podano warunek konieczny i wystarczający stabilności w sensie Hurwitza (Schura) kombinacji wypukłej dwóch wielomianów zespolonych tego samego stopnia. Warunki te są uogólnieniem pracy [2] i uzupełnieniem pracy [3].

A necessary and sufficient condition for stability of the convex combination of polynomials

Białas S.

Control and Cybernetics

2004

Vol. 33, no 4

589-597

This paper gives a necessary and sufficient condition for the Hurwitz (Schur) stability of the convex combination of the complex polynomials f1(x),f2(x),...,fm(x). It provides a generalization of the Ackermann, Barmish (1988). Barlett, Hollot, Huang (1988) and Bialas (1985).