Event-triggered feedback stabilization of switched linear systems via dynamic logarithmic quantization

This paper investigates the asymptotic stabilization for switched linear systems in the digital communication network. The event-triggered sampling and finite-level logarithmic quantization are combined to deal with the limited data-rate resources. The main challenge of such a work comes from two aspects: (1) Due to finite levels of actual quantizer, the quantizer saturation and nonzero steady-state error are hard to avoid. For this difficulty, the existing results on dynamic quantization are usually more suitable for uniform quantizer structure. (2) The interplay of system switching and event-triggered sampling leads to the mismatched switching of controllers. Coupling of these factors, the dynamic logarithmic quantizer (DLQ) and event-triggered mechanism (ETM) are rather complicated to build. To solve the above problems, we at first propose a novel DLQ by constructing a switching-dependent time-varying ellipsoid and developing a hybrid update policy of zoom function. This DLQ is co-designed by introducing a switching ETM. Then, a new quantization-dependent switching law is provided to guarantee the convergence of zoom function. Compared with the existing literature, this switching law has less restrictions and more flexibility. By our method, the DLQ will never saturate and the zoom function can be made converge to the origin with some carefully established parameters conditions. Thus, the switched system is asymptotically stabilized. At last, a comparison example is adopted to show the merits of our method and a practical system example is used to verify the effectiveness of the obtained results.