  This paper focuses on the computation of joint spectral radii (JSR), when the
involved matrices are sparse. We provide a sparse variant of the procedure
proposed by Parrilo and Jadbabaie, to compute upper bounds of the JSR by means
of sum-of-squares (SOS) relaxations. Our resulting iterative algorithm, called
SparseJSR, is based on the term sparsity SOS (TSSOS) framework, developed by
Wang, Magron and Lasserre, yielding SOS decompositions of polynomials with
arbitrary sparse support. SparseJSR exploits the sparsity of the input matrices
to significantly reduce the computational burden associated with the JSR
computation. Our algorithmic framework is then successfully applied to compute
upper bounds for JSR, on randomly generated benchmarks as well as on problems
arising from stability proofs of controllers, in relation with possible
hardware and software faults.
