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Certifying unstability of Switched Systems using Sum of Squares Programming. (arXiv:1710.01814v1 [math.OC])
来源于:arXiv
The joint spectral radius (JSR) of a set of matrices characterizes the
maximal asymptotic growth rate of an infinite product of matrices of the set.
This quantity appears in a number of applications including the stability of
switched and hybrid systems. A popular method used for the stability analysis
of these systems searches for a Lyapunov function with convex optimization
tools. We investigate dual formulations for this approach and leverage these
dual programs for developing new analysis tools for the JSR. We show that the
dual of this convex problem searches for the occupations measures of
trajectories with high asymptotic growth rate. We both show how to generate a
sequence of guaranteed high asymptotic growth rate and how to detect cases
where we can provide lower bounds to the JSR. We deduce from it a new guarantee
for the upper bound provided by the sum of squares lyapunov program. We end
this paper with a method to reduce the computation of the JSR of low rank
matrices to th 查看全文>>