Stability Analysis And Design For Control Systems With Multi-quantizers

In the classical feedback control theory, various signal and data of the process is assumed to be passed directly to the controller without data loss. With the development of modern industry, especially in the society which full of digital computer devices, however, in industrial practice it is not often the case. So the researchers applied signal quantized method to control field, its main purpose is to reduce the size of the information in the channel of control systems, save the system resources, facilitate system extension and monitoring. The overwhelm success of networked control system, especially in the industrial control and automation field, further aroused the researchers'interest on quantized feedback control, and obtained many works.It will cause lack of information and lost package in the transmission process of signal, and the quantization error, plus noise signal interference in the process of signal quantization. This phenomenon will affect system's performance index and the stability, so it has important realistic meaning and theoretical value to research the stability of system with multi-quantizers under the background of quantized feedback control.There are mainly three aspect results about this subject:First, we consider the analysis of state feedback and static output feedback for the discrete-time LTI (linear time-invariant) systems with two quantized signals. We assume that the state feedback and static output feedback have been designed for a discrete-time LTI system so that the closed-loop system is Hurwitz stable. For such quantized feedback control systems, we propose a state-dependent strategy for updating the quantizers'parameters, so that the system is asymptotically stable. Finally there are some numerical examples.Second, we consider analysis of quantized estimation and investigation of stability connection between estimation error system (EES) and quantized estimation feedback control system (QEFCS) with multi-quantized in this paper. We assume that there are two-quantized signals being passed to the estimator and the controller through network channels in the closed-loop NCS without noise. Using adjustable zoom quantizer parameters, Lyapunov-based quadratically stabilizable conditions of NCSs are presented, and then we extend the discussion to the system with noise. We also propose a method to disclose the stability connection of EES and QEFCS by the use of the connected invariant region sequences. Numerical example and simulation results demonstrate the effectiveness of the method.Finally, the estimator design of discrete-time networked control systems with multi-quantized output feedback is concerned. The estimator error is made minimum by the designed state estimator. At last, a numerical example is given to illustrate the effectiveness of the estimator.