Stability Analysis And Control Of Time Delay Systems Based On Convex Combination Technique

Time delay widely exists in various practical systems, because the existence of time delay often results in poor performance of control systems, even leads to instability. Therefore, the stability analysis and controller design of this type of systems have important implications. In this paper, the stability of several typical time-delay systems are studied. Through constructing proper LKF and various derivation methods, some less conservative stability criteria in LMI framework are derived. Then, we discuss the design method of state feedback controller of linear systems with input time delay. The main contents are as followed:1. Stability of linear system with time-varying delay is studied. Firstly, novel LKF with new variables and the cross-term relationship of different variables is constructed. By employing the quadratic convex combination technique, a new less conservative delay-dependent criterions is derived. Then by constructing the similar LKF and giving a new convex combination technique, a new improved delay-dependent criterions with less conservative is derived. Finally, two examples and simulations demonstrate that the methods are efficient.2. Consider the stability of linear system with interval time-varying delay. Because the lower limit of this kind of system is not zero, we introduce new variable about delay in LKF. Then using the reciprocally convex approach and convex combination technique, the new delay-dependent stability criteria is derived in terms of LMIs. Finally, two examples and simulations are used to demonstrate the method is effective.3. Analysis of the stability of neural networks with time-varying delay. Through introducing multiple integral expressed with high order scalar function, we construct a new augmented LKF. By improving the activation function condition, combined with the property of quadratic convex combination technique, a new less conservative criterion is derived.4. Based on the approach in the second chapter, we study the control of the delay system. For linear systems with input delay, a method of designing a state feedback controller and solving the controller gain is derived. Through the simulation, we know that the design of the controller can make the state of the system tends asymptotically stable.