Smooth Control of Asynchronously Switched Fuzzy Systems With Partly Stochastic Sojourn Time

This article investigates the smooth control problem of switched fuzzy systems, where the modes asynchronously switch under a partly stochastic sojourn time (PSST) switching signal, i.e., a duration of the sojourn time is governed by a random distribution. The formulated PSST switching signal is composed of a mode-dependent activated time and a duration subject to certain stochastic processes, which covers the conventional (average) dwell time (DT) switching signals or stochastic switching signals as special cases. Considering the measuring and computing delay in mode and membership degree identifying of the fuzzy switched systems, the asynchronous phenomena caused by unmatched case between control and system modes are included in the PSST switching signal, and a detected-mode-based Lyapunov candidate is formulated for the mean-square stability (MSS) and robustness analysis, which has not been considered before. To overcome the undesired control bump between adjacent modes, a multistage membership degree interpolation approach is proposed to obtain a smooth control transition after the asynchronous duration to carry out an anti-asynchronously stochastically smoothly switched fuzzy controller (A2S3-FC), unlike the existing literature that only considers part of the property of the practical systems. The effectiveness and the advantages of the proposed A2S3-FC are verified via a numerical example and a simulation of aerial manipulator attitude control.