Stability Analysis and Asynchronous Control of Almost Periodic Piecewise Linear Systems With Nonfixed Periods and Uncertain Subinterval Lengths.

This article investigates the stability analysis and asynchronous control issues of almost periodic piecewise linear systems (APPLSs) with nonfixed periods and uncertain subinterval lengths. Unlike strictly periodic piecewise dynamic systems in previous studies, we establish new sufficient conditions using Lyapunov stability theory because there is no fixed fundamental period and each subinterval length may vary. These conditions constrain the proportion of stable and unstable subintervals to guarantee stability. Given a maximum switching delay between the controller and the subsystems, we propose a state-feedback asynchronous control approach to ensure that the closed-loop system achieves exponential stability, even when a larger proportion of subsystems are unstable. This article also considers the possibility of rapid switching between subsystems. We develop three asynchronous controller design (ACD) algorithms for cases where some subsystems are unstabilizable, all subsystems are stabilizable, and all subsystems are unstabilizable. Finally, illustrative simulations using numerical examples and a tunnel diode circuit system verify the rationality and effectiveness of the proposed approach.