Stability Analysis Of The Networked Control System With Quantized Feedback

Networked control system (NCS) has been widely studied during the recent decades. Information theory and control theory are completely separated in the previous work. Actually, information influences control performance and control affects the quality of transmitted information. Therefore, it is conservative to ignore the relations between control and information in NCS. The relationship between quantization effect and the other network-induced problem, such as packet loss and time delays reflects the coupling between control and information.This paper investigates the relationship between the maximum allowable dropout bound and the quantization density. NCS is described as a time-delay switched system with constrained switching signals. A switched dynamic output feedback controller with prescribed disturbance attenuation level is designed via a cone complement linearization approach. A novel stability criterion is obtained by switched system theory. Furthermore, finding an appropriate quantization density used when packet dropout occurs is converted to an optimization problem. For zero-input and hold-input compensation strategy, this paper investigates stability of NCS subject to packet dropouts and quantization errors. Packet drop compensation strategy plays an important role in the performance of NCS. We propose two new stability analysis criterions for these two strategies via switched system method. The quantization density is designed to be switched according to network load condition, which is less conservative. Comparison of these two strategies is given in the sense of stability. By theoretical analysis, these two strategies apply for different scenarios and none of them can be claimed superior to the other. Numerical examples are derived for comparison of the two strategies.In this paper, the probability-guaranteed H∞ control of networked control systems (NCSs) with time-varying networked-induced delays is also addressed. The time-varying delays are modeled as polytopic uncertainty in the discrete-time model by a new approximation method based on real Jordan form. The system uncertainty lies in a parameter hyper-rectangle box which can shrink, i.e., the probability can be less than one with a better disturbance attenuation level. By the uniformity principle and the one-to-one correspondence between the time delays and the vertices of polytopic system, a sufficient condition for the NCS to achieve prescribed H∞ performance with given probability is derived. The controller synthesis problem is also proposed to meet the probabilistic requirement by solving a set of bilinear matrix inequalities (BMIs) iteratively. A uniform distribution is assumed for all the delays and thus the maximal probability guaranteeing the given performance can be calculated.