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- W2075606892 abstract "We consider switched linear systems of odes, x x(t)= A(u(t))x(t) where A(u(t)) ∈ A, a compact set of matrices. In this paper we propose a new method for the approximation of the upper Lyapunov exponent and lower Lyapunov exponent of the LSS when the matrices in A are Metzler matrices (or the generalization of them for arbitrary cone), arising in many interesting applications (see e.g. [9]). The method is based on the iterative construction of invariant positive polytopes for a sequence of discretized systems obtained by forcing the switching instants to be multiple of Δ(k)t where Δ(k)t → 0 as k → ∞. These polytopes are then used to generate a monotone piecewise-linear joint Lyapunov function on the positive orthant, which gives tight upper and lower bounds for the Lyapunov exponents. As a byproduct we detect whether the considered system is stabilizable or uniformly stable. The efficiency of this approach is demonstrated in numerical examples, including some of relatively large dimensions." @default.
- W2075606892 created "2016-06-24" @default.
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- W2075606892 date "2013-12-01" @default.
- W2075606892 modified "2023-09-22" @default.
- W2075606892 title "Polytope joint Lyapunov functions for positive LSS" @default.
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- W2075606892 doi "https://doi.org/10.1109/cdc.2013.6759965" @default.
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