Stability Analysis And Synthesis Of Time-Delay Systems Based On LMI Technique

In industrial production process, time delay phenomenon is very widespread when substance and energy are transmitted, and it is an inherent characteristic of physical systems. So, time-delay systems are usually used to describe ideally the delay phenomenon induced by the inertia effect of transmission and transference process. Time delay exists widely in many control systems, such as navigation, spaceflight, biology, zoology, economy and different engineering systems. It is shown that time delay is often the main reason of instability in many systems. Since its extensive application background, the research on time delay systems has received more and more attention recently. To ensure the stability and good dynamic performance of time delay systems, appropriate stability conditions and controller design methods should be presented rationally, which is a difficult topic with significant meaning.In the research of stability analysis and synthesis of time delay systems, by using the Leibnitz-Newton formula, the free weighting matrix method may reduce the conservatism induced by the fixed weighting matrix in the model transformation method, because of the simple principle of this method, it has received wide application. However, if the free weighting matrix method is used, many matrix variables will be introduced, which will lead to the increase of computational complexity. This thesis studies the problem of stability analysis of time delay systems, by using the Jensen inequality method, the computational complexity of the free weighting matrix method is reduced greatly. On the other hand, a delay decomposition method is proposed to deal with delay, since more information of state can be used, the obtained results are less conservative than the existing ones. These novel stability analysis methods for delay systems are used to study neural networks and networked control systems, and less conservative results are obtained.The details of this thesis are as follows. (1) For continuous-time linear systems with time delay, it is proved that the free weighting matrix method-based stability condition may be simplified, and the introduction of the Jensen integral inequality will introduce less computational complexity. The delay decomposition method is proposed to reduce the conservatism of the stability conditions, by using the delay decomposition method, more information of state can be used, and the estimation error of cross product items may be reduced.(2) For discrete-time linear systems with time delay, by defining a new Lyapunov function and using the Jensen inequality, new stability results with less computational complexity and less conservatism are presented. By using the delay decomposition method and considering the characteristics of discrete systems, the stability results are improved further.(3) Unlike the previous works, the activation functions are assumed in this thesis to be neither monotonic, nor differentiable, nor bounded. By defining a more general Lyapunov function, using the Jensen integral inequality and the delay decomposition method, the problem of stability analysis for neural networks with time-varying and constant delay are discussed, respectively, and new stability conditions with less conservatism are obtained. Compared with the existing results, the merits of the obtained results lie in their wide applicability, less conservatism and less decision variables, etc.(4) By taking the networked-induced time delay, packet dropout and signal quantizations into full consideration, the problems of H∞stability and H∞state feedback controller design of networked control systems are studied. Combining the new sector bound conditions of the logarithmic static and time-invariant quantizers with the Jensen inequality method, this thesis presents new H∞stability conditions. Different from the existing methods, since it is not needed to transfer the closed-loop system into a linear system with structure uncertainty, the complexity and conservatism introduced by the model transferring method can be avoided. Even only the state signal needs quantization or quantization is not needed for all signals, the new H∞stability condition is still less conservative and less complex than the existing results. Based on the H∞stability condition, an improved approach dealing with non-convex problem is proposed, and then a new H∞state feedback controller design method is also presented. Compared with the existing design methods, the newly proposed method can ensure better H∞performance.(5) For networked control systems with multiple packet transmission, this thesis considers the case that multiple packet transmission occurs in the sensor-to-controller channel and controller-to-actuator channel (which is not considered in the existing literature). By modeling the NCSs with multiple packet transmission as a special continuous-time linear system with multiple delays and using the Jensen inequality method, new stability results are presented. By simplifying the stability condition further, an improved parameter regulation method is proposed to simplify the state feedback controller design. Even reduced to the case of single packet transmission, the results of this thesis are less conservative, less computationally complex and more effective than the existing ones.Finally, the results of the dissertation are summarized and further research topics are pointed out.