It is a common thing that time delay phenomena exists in the control systems. Due to the existence of the time-delay item, the stability of the control system, time domain performance, frequency-domain performance will be influenced,So it is very important to study the time-delay systems for the analysis and design of the control system.This paper mainly by using the linear matrix inequality related theory, study the stability of the system with time-delay, control problems and guaranteed cost control problem,The paper puts forward the stability conditions, design the corresponding controller, and the numerical simulation results prove the feasibility of the method and the superiority.First of all, this paper summarizes the current research of systems with time delay, the linear matrix inequality (LMI) method of analysis. Then Introduced the basic knowledge of systems with time delay, system model. The paper focuses on the method of previous studies, proposed the, the improved theorem. Second, this paper studies the stability of the system with time-delay. Divided into three kinds of typical systems with time delay, delay-dependent system, delay-independent system system and parameter uncertain time-delay system. The stability criterion are given, and into the linear matrix inequality the feasibility problems to solve. The improved algorithm has smaller conservative, in the process of simulation proved the validity of the proposed method.And then, the research of the delay system Hâˆžcontrol problem. Respectively memoryless state feedback controller and dynamic output feedback controller are designed, the closed-loop control system is asymptotically stable, and the performance of system is less than a given value norm. Through the linear matrix inequality, the parameters of the matrix to controller is solved, the numerical simulation results prove the superiority of the controller design method.Finally,this paper studies the guaranteed cost control systems with time delay. Memoryless state feedback controller is designed so that the closed-loop system is asymptotically stable, and the second cost Hâˆžfunction has the upper bound of the smallest. Guaranteed cost control systems with time delay has important application value of the performance optimization. In the solving process, by using the linear matrix inequality feasibility problems,controller parameter matrices is got, and gives a real fighter example, the simulation results prove the validity of the proposed method... |