We introduce a novel framework for the stability analysis of discrete-timelinear switching systems with switching sequences constrained by an automaton.The key element of the framework is the algebraic concept of multinorm, whichassociates a different norm per node of the automaton, and allows to exactlycharacterize stability. Building upon this tool, we develop the firstarbitrarily accurate approximation schemes for estimating the constrained jointspectral radius r, that is the exponential growth rate of a switching systemwith constrained switching sequences. More precisely, given a relative accuracya > 0, the algorithms compute an estimate of r within the range [r; (1 + a)r].These algorithms amount to solve a well defined convex optimization programwith known time-complexity, and whose size depends on the desired relativeaccuracy a > 0.
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