Analysis Methods, Based On Robust Absolute Stability Of The Lmi Interval Lurie Control Systems

In the analysis and synthesis of control systems, the research of absolute stability for Lurie control systems is very important for the analysis and design of nonlinear control systems, and set store by scholars of the inside and outside. In the application, the uncertainty of parameters is in existence diffusely in many control systems. So the disquisition of the robust absolute stability for Lurie control systems seems more important. And the interval system is important one of the cases. In this paper, we will study and discuss the robust absolute stability of the interval Lurie control system and the interval Lurie control system with time-delay respectively, bring forward the analysis approach for robust absolute stability based on linear matrix inequality (LMI).Based on the conventional Lurie-type Lyapunov function method, three methods are adopted in this paper: common inequality method, port matrix method and equivalent description method. We analyze and discuss the two kinds of control systems including the common interval Lurie control system and the interval Lurie control system with time-delay utilizing the above three methods. For the common inequality method, a LMI for positive definite matrix and the coefficients of the integral items of the Lurie-type Lyapunov function is given using the inequality about interval matrix. The Lyapunov function constructed by the solution of the LMI is adopted to guarantee the robust absolute stability of the system. For the port matrix method, a LMI for positive definite matrix and the coefficients of the integral items of the Lurie-type Lyapunov function based on the relationship between the stable problem of the interval system and the stable research of its port matrix is given, and the Lyapunov function constructed by the solution of the LMI is adopted to guarantee the robust stability of the systems. For the equivalent description method of interval matrix, a LMI for positive definite matrix and the coefficients of the integral items of the Lurie-type Lyapunov function is given by adopting the equivalent description of interval matrix, and the Lyapunov function constructed by the solution of the LMI is adopted to guarantee the robust stability of the systems.For the common interval Lurie control system and the interval Lurie control system with time-delay, not only the case of the infinite sector but also the finite sector is discussed by the three methods in this paper, and the conclusion is applicable to the case of multiple non-linearity. An example is provided in every chapter to demonstrate the effectiveness of the proposed method, and the relation between the size of the sector and the robustness is analyzed.