Sampled-Data Asynchronous Control for Switched Nonlinear Systems With Relaxed Switching Rules

IEEE Transactions on Cybernetics(2022)

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Abstract
This article investigates the problem of quantized sampled-data control for continuous-time switched Takagi–Sugeno (T–S) fuzzy systems with the asynchronous phenomenon. First, considering that the system and controller modes could not be perfectly synchronized all the time, we study possible cases of mode mismatching by exploiting the average dwell time (ADT) switching strategy. Since the fact that a minimum dwell time of each subsystem is not required in the ADT switching rule, multiple system switching is allowed within one sampling interval, which overcomes the limitation of at most once switching during any sampling interval in existing works. Second, the asynchronous premise variables between the fuzzy system and fuzzy controller are taken into consideration in the quantized sampled-data control scheme. Then, by virtue of the Lyapunov function approach, we obtain sufficient conditions to guarantee that the asynchronously switched T–S fuzzy system is exponentially stable with quantized sampled-data input. Furthermore, the weighted $L_{2}$ -gain is discussed for the system under external disturbance, and an $H_{\infty }$ state feedback controller is correspondingly designed with prescribed disturbance attenuation. Finally, the validity and advantage of the proposed methods are illustrated by two examples.
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Key words
Algorithms,Computer Simulation,Feedback,Nonlinear Dynamics
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