Data-based computation of stabilizing minimum dwell times for discrete-time switched linear systems
This work addresses stability analysis for switched systems in control engineering, but it is incremental as it builds on existing Lyapunov-based methods without introducing a fundamentally new approach.
The authors tackled the problem of computing stabilizing minimum dwell times for discrete-time switched linear systems without requiring explicit state-space models, achieving this through an algorithm that uses finite state trajectory traces to design multiple Lyapunov functions and compute relevant scalars.
We present an algorithm to compute stabilizing minimum dwell times for discrete-time switched linear systems without the explicit knowledge of state-space models of their subsystems. Given a set of finite traces of state trajectories of the subsystems that satisfies certain properties, our algorithm involves the following tasks: first, multiple Lyapunov functions are designed from the given data; second, a set of relevant scalars is computed from these functions; and third, a stabilizing minimum dwell time is determined as a function of these scalars. A numerical example is presented to demonstrate the proposed algorithm.