Stability Analysis And Control Of Time Delay Systems Based On LMI

The delay widely exists in the actual system and leads to instability which causes a lot of difficulties in the stability research and control of the system. Therefore, the stability analysis and control of the time-delay systems has important theoretical significance and practical value. In this paper, the stability of some typical time-delay systems is studied. By constructing suitable Lyapunov functional, combined with the integral inequality method, free weight matrix method and delay decomposition method, we obtain the system’s stability criteria respectively which are less conservative and discuss the design method of state feedback controller of linear systems with time delay. The main contents are as followed:(1) Studies the stability of linear time-delay systems. By the introduction of the new variable and the cross-term relationship of the variable, we contruct new Lyapunov functional, combined with integral inequality and free weight matrix method respectively, obtain less conservative stability criteria based on LMI. Futhermore, by using the property of quadratic convex function, a new less conservative delay-dependent criterion is derived. The simulation examples demonstrate the superiority of the method which is used.(2) The stability of Lurie systems with time delay is studied. When we construct Lyapunov functional, we add the cross-term relationship of many variables which are ignored in the previous literature. By taking advandage of delay decomposition approach, combined with free weight matrix method and integral inequality method, we obtain less conservative stability criteria based on LMI.(3) Analysis of the stability of delayed neural networks. Through the introduction of new integral and the cross-term relationship among variables, we construct a new Lyapunov functional. By improving the activation function condition, combined with the property of quadratic convex function, a new less conservative criterion in terms of LMI is derived.(4) Finally, we discuss the control of the delay system based on the above research.We derive the design method of state feedback controller with the input delay or with the state delay, and give guidelines for solving the controller gain. Through the analysis of the simulation, we know that the design of the controller can make the state of the system tends asymptotically stable, which also certifies the effectiveness of the method.