We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded both from below (the guaranteed dwell-time) and from above (the maximal time of a single mode). The presence of upper bounds makes this problem quite different from the classical case. For instance, a stable system can now consist of unstable matrices, it may not possess Lyapunov functions, etc. We introduce the concept of a convex Lyapunov multifunction with discrete monotonicity. Its existence, as well as the existence of invariant norms, are proved. We also establish a modified Berger-Wang formula over periodizable switching laws. Those results provide a method of computation of the Lyapunov exponent with an arbitrary precision. Its efficiency is shown in numerical examples.
Stability of Continuous Time Linear Systems with Bounded Switching Intervals
Protasov, Vladimir Yu.;
2023-01-01
Abstract
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded both from below (the guaranteed dwell-time) and from above (the maximal time of a single mode). The presence of upper bounds makes this problem quite different from the classical case. For instance, a stable system can now consist of unstable matrices, it may not possess Lyapunov functions, etc. We introduce the concept of a convex Lyapunov multifunction with discrete monotonicity. Its existence, as well as the existence of invariant norms, are proved. We also establish a modified Berger-Wang formula over periodizable switching laws. Those results provide a method of computation of the Lyapunov exponent with an arbitrary precision. Its efficiency is shown in numerical examples.Pubblicazioni consigliate
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