Stability Analysis Of Network-Based Control Systems

In networked control systems (NCSs), components (including plants, sensors, con-trollers and actuators, etc) communicate via communication networks. The introduction of networks overcomes the shortcomings, such as more wiring, high costs, hard mainte-nance and installation, etc, introduced by traditional point-to-point wiring systems. On the other hand, communication networks which are shared by these components also bring some challenges, including quantization error, random delay, packet dropouts, multiple packet transmission and so on. In this paper, we will study the NCSs with mul-tiple network-induced problems occurring simultaneously.This paper studies the quantized output feedback control of networked control sys-tems with packet dropout existing in both sensor-controller and controller-actuator chan-nels. The stochastic switching signal of quantization density and quantized dynamic out-put feedback controller are designed to be functions of successive packet loss number in both sensor-controller and controller-actuator channels. The packet dropouts over the two links are modelled as two independent Markov chains and the late arrival packets are considered in the model. A stability criterion relying on quantization density and succes-sive packet loss number is proposed by using the stochastic system theory and the quan-tized output feedback controller is obtained via a cone complement linearization ap-proach. Then, this paper study the case where multiple sensors and actuators are used and geographically distributed in NCSs. Each separate quantizer is located on every node, namely, one sensor one quantizer, one actuator one quantzier. The measurements of each sensor and inputs of each actuator experience different successive packet dropout pro-cesses and will be quantized at different quantization levels which are decided by the re-lated successive packet dropout number. A sufficient condition is derived for the NCSs with multiple packets transmission to be stochastically stable with a prescribed H∞ noise attenuation performance by using the Lyapunov-Krasovskii function. And the sto-chastically switched quantized dynamic output feedback controller is obtained. In this paper, we also study an event-triggered communication scheme for a class of dis-crete-time linear NCSs with quantized error and time-varying communication delay. The output measurement signals of the plant are sampled in a periodic manner, and an event-triggered communication condition is applied to choose those only necessary data to be transmitted after being quantized. The closed-loop system with a dynamic output feedback controller is modeled as an event-triggered networked systems with interval time-varying delays based on the time delay system approach. Sufficient conditions of the stochastic stability with a prescribed H∞ performance level is established in terms of linear matrix inequalities (LMIs). By using a cone complement linearization approach the controller and event-triggering parameters are co-designed. Finally, a numerical ex-ample is provide to illustrate the effectiveness of the designed method.