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1

Schur stability of the convex combination of complex polynomials

Białas S., Białas M.

Control and Cybernetics

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2010

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Vol. 39, no 2

551-558

EN

This paper gives a necessary and sufficient condition for Schur stability of the convex combination of complex polynomials. It is a generalization of the work by Ackerman and Barmish (1988).

2

Stability of the convex combination of polynomials

Góra M.

Control and Cybernetics

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2007

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Vol. 36, no 2

425-442

EN

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.

3

Criterions for the stability of the convex combination of polynomials

Zalot E.

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

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2006

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T. 10, z. 1

87-95

EN

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].

PL

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].

4

A sufficient condition for Schur stability of the convex combination of the polynomials

Białas S.

Opuscula Mathematica

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2005

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Vol. 25, no. 1

25-28

EN

In this paper is given a simple sufficient condition for Schur stability of the convex combination of the real polynomials.

5

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

Białas S.

Control and Cybernetics

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2004

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Vol. 33, no 4

589-597

EN

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).

6

Robust Stability of D-symmetrizable Hyperbolic Systems

Ziółko M., Białas S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2001

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vol. 49, nr 1

167-176

EN

The systems under consideration are governed by a set of first-order linear partial differential hyperbolic equations together with boundary conditions. The Lyapunov method is used to verify the stability of the initial-boundary value problem. Necessary and sufficient conditions for stability are obtained under the assumption that the matrix coefficients in the differential equations and in the boundary conditions are D-symmetrizable. The considered systems have an interesting property: Hurwitz type stability and Schur type stability occur in one system simultaneously. The stability of the conditions type system is a stability of wave propagation. The stability of the discrete type system is a stability of the boundary feedback and the boundary reflections. Necessary and sufficient conditions for the robust stability of an initial-boundary value problem are obtained for the case where the matrix coefficients belong to a convex hull of stable and D-symmetrizable matrices.