Stability and Stabilization of Almost Periodic Piecewise Linear Systems With Dwell Time Uncertainty

This article is dedicated to the stability and stabilization of almost periodic piecewise linear systems (APPLSs) with the uncertain dwell time of subsystems. Taking into account the uncertainty in dwell time for the first time, a novel mixed-mode time-varying Lyapunov function is constructed. A sufficient condition is proposed to guarantee the exponential stability of the system, where the switching instants over each period are unknown and inaccessible except their bounds. Moreover, a periodic time-scheduled state-feedback control approach is developed to stabilize the APPLS affected by dwell time uncertainty and possibly unstabilizable subsystem dynamics. A stabilizing controller design algorithm is provided to compute the time-varying gains. The effectiveness of the proposed approach is illustrated via a numerical example involving comparative case studies.