An entropy-based bound for the computational complexity of a switched system
Author(s)Legat, Benoit; Parrilo, Pablo A; Jungers, Raphael M
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© 2019 IEEE. The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and hybrid systems. A popular method used for the stability analysis of these systems searches for a Lyapunov function with convex optimization tools. We analyze the accuracy of this method for constrained switched systems, a class of systems that has attracted increasing attention recently. We provide a new guarantee for the upper bound provided by the sum of squares implementation of the method. This guarantee relies on the $p$-radius of the system and the entropy of the language of allowed switching sequences. We end this paper with a method to reduce the computation of the JSR of low-rank matrices to the computation of the constrained JSR of matrices of small dimension.
DepartmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE Transactions on Automatic Control
Institute of Electrical and Electronics Engineers (IEEE)