A Gel'fand-type spectral radius formula and stability of linear constrained switching systems

Abstract

Using ergodic theory, in this paper we present a Gel'fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup $\bS^+$ restricted to a subset that need not carry the algebraic structure of $\bS^+$. This generalizes the Berger-Wang formula. Using it as a tool, we study the absolute exponential stability of a linear switched system driven by a compact subshift of the one-sided Markov shift associated to $\bS$.

16 pages; to appear in Linear Algebra and its Applications

References in corpus (1)

• The generalized Berger-Wang formula and the spectral radius of linear cocycles

Cited by in corpus (1)

• Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equations