  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.
