Containing Uncertain Time-delay Lurie System Stability Analysis

Lurie control system is a nonlinear control system, and has a strong applica-tion background in many fields including aerospace vehicle control, aviation and aerospace control, hydraulic control and so on. Therefore, it is of great significance to study intensivelyFor Lurie system, there are two main methods to study its stability:Popov frequency domain method and Lurie type Lyapunov functional method.Unlike to Popov frequency domain method can not handle uncertain Lurie systems with mul-tiple nonlinear feedback link. Lyapunov functional method can handle any linear or nonlinear system with varying time-delay and parameter uncertainty. So the Lurie type Lyapunov functional method is used commonly. This method need to construct appropriate Lyapunov functional, and then prove that its derivative is negative defi-nite along the trajectory of the system. When analyzing the stability of Lurie system with time-delay, conventional Lurie type Lyapunov functional method is still conser-vative. However, delay decomposition approach by dividing the time delay interval into several sub-interval, each subinterval uses different Lyapunov matrix, reduces the conservative further.In this thesis, we study intensively the robust absolute stability for uncertain Lurie system of neutral type and for uncertain Lurie singular system with time-varying delay. The main work is as follows:1. we study the robust absolute stability for uncertain Lurie system of neu-tral type with time-varying delay. By dividing delay interval into two sub-interval, constructing the corresponding Lyapunov functional, and using the linear matrix inequality approach, some sufficient conditions are provided to ensure its robust absolute stability. Because these conditions express are linear matrix inequalities, it is easy to implement using the LMI toolbox of Matlab software. Numerical ex-amples show that the given conditions increase the maximum time delay upper bound(hmax), and reduce the conservative further, thus verify the effectiveness of the conditions.2. we study the robust absolute stability for uncertain Lurie singular system with time-varying delay. Since the existing stability condition built by using con-ventional Lurie type Lyapunov functional is still conservative. To further reduce the conservative, we construct a new Lyapunov functional using delay decomposition method, and combining with Jenson inequality, give some sufficient conditions to guarantee the system robust absolute stability. Numerical experiments, illustrates the superiority of the given conditions.