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arXiv · 1807.03965

Approximation of The Constrained Joint Spectral Radius via Algebraic Lifting

Xiangru Xu·Behcet Acikmese
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Abstract

This paper studies the constrained switching (linear) system which is a discrete-time switched linear system whose switching sequences are constrained by a deterministic finite automaton. The stability of a constrained switching system is characterized by its constrained joint spectral radius that is known to be difficult to compute or approximate. Using the semi-tensor product of matrices, the matrix-form expression of a constrained switching system is shown to be equivalent to that of a lifted arbitrary switching system. Then the constrained joint/generalized spectral radius of a constrained switching system is proved to be equal to the joint/generalized spectral radius of its lifted arbitrary switching system which can be approximated by off-the-shelf algorithms.

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Xiangru Xu, Behcet Acikmese. 2018-07-11. Approximation of The Constrained Joint Spectral Radius via Algebraic Lifting. https://arxiv.org/abs/1807.03965

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