Approximation of The Constrained Joint Spectral Radius via Algebraic Lifting. (arXiv:1807.03965v1 [math.OC])

A linear constrained switching system is a discrete-time linear switched system whose switching sequences are constrained by a deterministic finite automaton. As a characterization of the asymptotic stability of a constrained switching system, the constrained joint spectral radius is difficult to compute or approximate. Using the semi-tensor product of matrices, we express dynamics of a deterministic finite automaton, an arbitrary switching system and a constrained switching system into their matrix forms, respectively, where the matrix expression of a constrained switching system can be seen as the matrix expression of a lifted arbitrary switching system. Inspired by this, we propose a lifting method for the constrained switching system, and prove that the constrained joint/generalized spectral radius of the constrained switching system is equivalent to the joint/generalized spectral radius of the lifted arbitrary switching system. Examples are provided to show the advantages of the p 查看全文>>