Switching systems with dwell time: Computing the maximal Lyapunov exponent

We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These are reformulated as special cases a general class mixed (discrete–continuous) linear switching on graphs, in which some modes correspond to discrete actions and others evolutions. Each action has its own positive weight accounts for time-duration. develop theory the systems; particular, we prove existence an invariant Lyapunov norm graphs structure various cases, including discrete-time have inhomogeneous time durations. This allows us adapt recent methods joint spectral radius computation (Gripenberg’s algorithm Invariant Polytope Algorithm) compute exponent graphs.