On Finite-Time Stability For Quantized Feedback Systems

With the rapid development of the technology of network communication and computer, more and more scholars pay close attention to the study of network control systems. In view of the limited bandwidth and the information security in network control systems, quantization is introduced and has been widely used. In the past, investigations on quantized systems are restricted to the property of asymptotic stabilization,little work has been done for the finite-time stability. Considering the wide application of quantized systems and the finite-time stability in practice, it motivates us to investigate the finite-time stability and stabilization problems for systems with quantized signals. The main research results of this thsis are as follows:First, we consider the issue of finite time stabilization of linear systems under quantization. Static quantizer is adopted, and the range and the error bound of the quantizer are given. We make use of the Lyapunov approach to derive a criterion guaranteeing the state trajectory does not exceed a certain threshold over a pre-specified finite-time interval.Second, for nonlinear systems, the state quantization and the input quantization are utilized to establish sufficient conditions which ensure that the nonlinear quantized systems are finite-time stable.Finally, we deal with the finite-time stability problem of linear quantized systems with actuator fault. Here dynamic quantizer is adopted. We derive a sufficient condition that makes systems to be finite-time stable. Based on the way of dynamic quantization,we obtain a recurrence method in the process of proof, which is convenient for the conclusion deduced.Some numerical simulations demonstrate the effectiveness of above results.