A limit formula for joint spectral radius with p-radius of probability distributions

作者：Ogura M^*; Martin C F

来源：Linear Algebra and Its Applications, 2014, 458: 605-625.

DOI：10.1016/j.laa.2014.06.034

• Joint spectral radius
• p-Radius
• Lyapunov functions
• Absolute exponential stability

In this paper we show a characterization of the joint spectral radius of a set of matrices as the limit of the p-radius of an associated probability distribution when p tends to infinity. Allowing the set to have infinitely many matrices, the obtained formula extends the results in the literature. Based on the formula, we then present a novel characterization of the stability of switched linear systems for an arbitrary switching signal via the existence of stochastic Lyapunov functions of any higher degrees. Numerical examples are presented to illustrate the results.

• 出版日期2014-10-1