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1
Content available remote 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.
2
Content available 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].
3
Content available A necessary and sufficient condition for sigma-Hurwitz stability of the convex combination of the polynomials
Białas S.
Opuscula Mathematica
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2005
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Vol. 25, no. 2
165-168
EN
In the paper are given a necessary and sufficent condition for sigma-Hurwitz stability of the convex combination of the polynomials.
4
Content available remote Robust performance of a class of control systems
Wang L.
Control and Cybernetics
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2004
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Vol. 33, no 1
71-83
EN
Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications of these results in testing of robust strict positive realness of real and complex interval transfer function families are also presented.
5
Content available remote A sufficient condition for Hurwitz stability of the convex combination of two matrices
Białas S.
Control and Cybernetics
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2004
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Vol. 33, no 1
109-112
EN
The paper provides a simple sufficient condition for Hurwitz stability of the convex combination of two real matrices.
6
Content available remote 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).
7
Content available remote 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.
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