Finite-time H∞ control of switched linear systems with unstable subsystems based on mode-dependent average dwell time

This paper investigates the finite-time boundedness (FTB) and robust control of switched linear systems with unstable systems (SLS-US) by utilizing mode-dependent average dwell time (MDADT). Due to the consideration of the presence of unstable subsystems in our work, this paper distinguishes between switching signals in stable and unstable cases based on the characteristic of allowing each subsystem to have independent average dwell time (ADT) according to MDADT. Stable subsystems utilize slow MDADT (SMDADT), whereas unstable subsystems employ fast MDADT (FMDADT). This switching behaviour effectively addresses the energy increment caused by the divergence of unstable systems. This paper presents the necessary conditions to achieve the H∞ performance index within the SLS-US. Moreover, it outlines the design of a state-feedback controller aimed at resolving the H∞ control problem within the closed-loop system. The verification of the proposed result is conducted through linear matrix inequalities (LMIs). Finally, the paper confirms the practicality of the proposed theory.