Matrisler ailesinin anti-Schur kararlılığı

ISSN: 1300-2708
Yayın Aralığı: Yılda 4 Sayı
Yayıncı: FIRAT ÜNİVERSİTESİ

Bu çalışmada, kompakt, konveks kompleks matrisler ailesinin anti-Schur kararlılığı için gerek ve yeter şartlar verilmiştir. Sonlu tane anti-Schur kararlı kompleks matrisin konveks zarfının oluşturduğu kümenin anti-Schur kararlı olması için uç nokta teoremi elde edilmiştir.

Anti-Schur stability of a family of matrices

In this paper, necessary and sufficient conditions for the anti-Schur stability of a compact, convex family of complex matrices are given. An extreme point theorem which guarantees the anti-Schur stability of the convex hull of a finite set of anti-Schur stable complex matrices is obtained.

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1. Johnson, C. R. (1976). A Local Lyapunov Theorem and the Stability of Sums, Linear Algebra Appl., 13, 37-43.
2. Cohen, N., Lewkowicz, I. (1993). A Necessary and Sufficient Criterion for the Stability of a Convex Set of Matrices, IEEE Trans. Automat. Control, 38 (4), 611-615.
3. Cohen, N., Lewkowicz, I. (2000). A Characterization of Convex Cones of Matrices with Constant Regular Inertia, Linear Algebra Appl, 318, 23-33.
4. Monov, V. V. (1999). On the Spectrum of Convex Set of Matrices, IEEE Trans. Automat. Control 44 (5), 1009-1012.
5. Dzhafarov, V., Büyükköroğlu, T. (2006). On the Stability of a Convex Set of Matrices, Linear Algebra Appl, 414, 547-559.
6. Gantmacher, F. R. (1959). The Theory of Matrices, Vol II., Chelsea Publishing Company, New York.
7. Aubin, J.P. (1993). Optima and Equilibria: An Introduction to Nonlinear Analysis, Springer, Berlin.