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Switching systems with dwell time: computing the maximal Lyapunov exponent
Nonlinear Analysis: Hybrid Systems. 2021. Vol. 40. Article 101021.
Chitour Y., Guglielmi N., Protasov V., Sigalotti M.
We study asymptotic stability of continuous-time systems with mode-dependent guaranteed
dwell time. These systems are reformulated as special cases of a general class
of mixed (discrete–continuous) linear switching systems on graphs, in which some
modes correspond to discrete actions and some others correspond to continuous-time
evolutions. Each discrete action has its own positive weight which accounts for its timeduration.
We develop a theory of stability for the mixed systems; in particular, we prove
the existence of an invariant Lyapunov norm for mixed systems on graphs and study
its structure in various cases, including discrete-time systems for which discrete actions
have inhomogeneous time durations. This allows us to adapt recent methods for the
joint spectral radius computation (Gripenberg’s algorithm and the Invariant Polytope
Algorithm) to compute the Lyapunov exponent of mixed systems on graphs.
Publication based on the results of:
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