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