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

作者：Dai Xiongping^*

来源：Linear Algebra and Its Applications, 2012, 436(5): 1099-1113.

DOI：10.1016/j.laa.2011.07.029

• Joint/generalized spectral radius
• Gel'fand-type spectral-radius formula
• Linear switched system
• Asymptotic stability

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 S+ restricted to a subset that need not carry the algebraic structure of S+. 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 S.

• 出版日期2012-3-1
• 单位南京大学