H_∞ Control And Networked Control For Linear Systems With Dual-rate Sampling

The H∞ control and networked control for linear systems with dual-rate sampling are studied in this thesis. The dual-rate sampling refers to sampling the output variables of the system by using two sensors with different sampling rates. Due to the advantages of multi-rate sampling, e.g., improving system performance, resistant to external disturbance, suitable for the complex practical system, the multi-rate sampling scheme is widely con-cerned in the practical applications. The common method used for modeling of multi-rate sampled-data systems is the lifting technique, which is to transfer the multi-rate linear sys-tem to a higher dimensional linear time-invariant discrete system. Considering the negative effects of the lifting technique on computational complexity and the restrictive in the system with constraints such as the network, random disturbance and nonlinearity, an input-delay method is proposed for system modeling. The main research contents of this thesis contain two parts:the first part is the study of the dual-rate sampling H∞ control for a kind of linear time-invariant systems in the physical environment, the second part is the event-triggered dynamic output feedback control for networked dual-rate sampled-data control systems. The work of this thesis is organized as follows:(1) The first chapter gives the introduction of the sampled-data systems, network control systems and the research status at home and abroad, then introduces the main research contents of this thesis.(2) The second chapter considers the modeling and analysis of the dual-rate sampling H∞ control for a kind of linear time-invariant systems in the physical environment. Ac-cording to whether the sampled information of the system output variables under dif-ferent sampling rates is available simultaneously, a switched controller is constructed to control the system, and the sampled information at different time is used fully and realtimely. By using the input-delay method, the closed-loop system is modeled as a pe-riodic switched control system with different time-varying input delays. The stability of the system is proved based on the Lyapunov-Krasovskii theory, some delay-dependent criteria on the exponential stability and the existence of the switched controller are proposed. Finally, a simulation example is proposed to show the effectiveness of the proposed scheme in this chapter.(3) In the third chapter, the dynamic output feedback control of dual-rate sampled-data control system in a network environment is considered. In the system, the sampled-data of the sensors are transmitted to the controller through a communication network with time-varying delay. In order to ease the burden of network, some event-triggering mechanisms are added at the sensors-side to reduce the transmission of redundant infor-mation, which improves the network utilization. A dynamic output feedback controller is designed to control the system, which fully uses the real-time data transmitted through the network. Considering the network-induced delay, by using the input-delay method, the resulting system is modeled as a closed-loop control system with two different input delays. According to the Lyapunov-Krasovskii theory, a delay-dependent stability cri-terion is given, and the controller design method is presented. A simulation experiment is selected to verify the effectiveness of the proposed method in this chapter.(4) In the fourth chapter, we summarize the present research work, and make a prediction about the future work.