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Abstract: We show that the joint spectral radius of a set of matrices is strictly increasing as a function of the data in the sense that if a set of matrices is contained in the relative interior of the convex hull of an irreducible set of matrices, then the joint spectral radius of the smaller set is strictly smaller than that of the larger set. This observation has some consequences in the theory of time-varying stability radii and their calculation. We show by example that, strict monotonicity... (Update)
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BibTeX entry: (Update)
@misc{ wirth-monotonicity,
author = "Fabian Wirth",
title = "A Monotonicity Property of the Joint Spectral Radius",
url = "citeseer.ist.psu.edu/wirth04monotonicity.html" }
Citations (may not include all citations):640 Princeton University Press (context) - Rockafellar - 1970
52 Bounded semigroups of matrices (context) - Berger, Wang - 1992
40 Lyapunov indicator of discrete inclusions (context) - Barabanov - 1988
16 The generalized spectral radius and extremal norms - Wirth - 2002
14 Constructive Nonsmooth Analysis (context) - Demyanov, Rubinov - 1995
8 Analysis of the Local Robustness of Stability for Flows - Wirth - 1998
8 On irreducibility of semigroups of compact operators (context) - Radjavi - 1990
5 Irreducible semigroups with multiplicative spectral radius (context) - Omladi, Radjavi - 1997
4 Robustness of nonlinear systems and their domain of attracti.. - Wirth - 2000
2 A linearization principle for robustness with respect to tim.. - Wirth - 2002
2 volume 178 of Graduate Texts in Mathematics (context) - Clarke, Ledyaev et al. - 1998
1 The generalized spectral radius is strictly increasing - Wirth - 2003
1 manuscript accepted for publication by Lecture Notes in Math.. (context) - Wirth, for
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Characterizing Controllability Probabilities of Stochastic .. - Camilli, Grüne, Wirth (2004) (Correct)
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