Efficient Method for Computing Lower Bounds on the $p$-radius of Switched Linear Systems

Abstract

This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear systems and the equilibrium analysis of switched linear economical models, algorithms for computing the $p$-radius are only available in a very limited number of particular cases. The proposed lower bounds are given as the spectral radius of an average of the given matrices weighted via Kronecker products and do not place any requirements on the set of matrices. We show that the proposed lower bounds theoretically extend and also can practically improve the existing lower bounds. A Markovian extension of the proposed lower bounds is also presented.

References in corpus (1)

• The Berger-Wang formula for the Markovian joint spectral radius

Cited by in corpus (4)

• An entropy-based bound for the computational complexity of a switched system
• Linear dynamical systems on graphs
• Fast approximation of the $p$-radius, matrix pressure or generalised Lyapunov exponent for positive and dominated matrices
• Kronecker weights for instability analysis of Markov jump linear systems