Practical Stability Analysis And Controller Design Of Networked Control Systems

Networked control systems (NCS) are a research field with strongly practical background and facing multifarious problems during the study process. In NCS, stability is the structural characteristic of the system, relating to the system can work regularly or not. It is considered one of the most important problems in the analysis and design of NCS, which includes the stability of network itself and the control system. Embracing asymptotic stability and exponential stability, the definition of the stability of NCS is similar to the traditional system. Owing to their own characteristics, there are many situations that should be taken into account when analyzing the stability of the system. Different models have different definitions of stability.Both asymptotic stability and exponential stability just belong to qualitative theory, however, practical stability is a quantitative theory of stability. Generally speaking, the problem that practical stability study is that given a time interval (limited or unlimited) and an initial condition region in advance to determine whether the system’s trajectory can belong to the region. That is to say, it does not consider whether the entire states tend to the balance point, while only considering whether the initial states and the entire states are located in the given regions. Though the researches of stability of traditional systems have achieved plentiful results, there are few reports on the research of practical stability of NCS. As a result, it embraces enormously research significations. The main results of this paper are as follows.(1) We promote the basic concepts, research methods and results of practical stability of the normal system. The practical stability of linear discrete systems and linear discrete systems with delay is introduced respectively. Then a sufficient condition which makes sure the system to be practically stable is given by constructing a Lyapunov function.(2) The NCS model based on uncertain delay is established. Then we utilize the above theorem, combining with practical stability theory and LMI techniques to analyze the practical stability of the system.(3) The NCS model based on network delay and packet loss is established. This model can be seen as an asynchronous dynamic switching system. Besides, we discuss the influence of switching system to the practical stability. By using the theory of NCS, practical stability, and LMI techniques, some sufficient conditions of practical stability can be drawn.(4) Basing on the above two models, we design the state feedback controller and give the relevant computer algorithm, which verifies the correctness of the conclusions.(5) The effect that network characteristics have on practical stability is given. Additionally, we conclude the main research work of this paper and point out the possible improvement directions.