Finite time stability condition for switched systems under restricted switching

Finite-time stability (FTS) has garnered considerable attention within the realm of control theory as a subject of active research. The objective of this paper is to explore the FTS of switched systems by employing a novel approach that relies on the concept of average dwell time (ADT). The ADT serves as a metric for quantifying the average duration a system remains in a specific mode prior to transitioning to a different mode. In this context, a condition that establishes the sufficiency of achieving FTS for a switched system has been derived in terms of the ADT and the corresponding Lyapunov function. Numerical simulations have been conducted to assess the efficacy of the proposed approach. Achieving a stable state within a specific time frame is crucial in many practical applications to meet desired performance requirements. The outcomes of this study have the potential to advance the development of more effective and reliable control systems across various engineering domains, including robotics, power systems, and transportation systems, which are often modeled as switched systems.