System Sample Value Feedback Stabilization Study

Sampled-data widely exists in computer control systems, hybrid systems and embedded control systems, etc. Because of the discreteness of sampled-data and the continuity of process, the discrete and continuous signals in the systems overlap each other, which makes it more difficult for the system stability analysis.In the thesis, we mainly research the state feedback and the output feedback stabilization problem for the sampling system. We put forward the controller design scheme based on the sampling state feedback and the observer design scheme based on the output sampling data, respectively. To solve the discretization problem caused by the sampled-data, we introduce a control input time-delay method to solve the problem of discrete and continuous coexist, which makes the sampling systems become the continuous time systems based on the input delay.The main theory is the Lyapunov stability theory for system stability analysis and system feedback stabilization implementation. Through constructing Lyapunov-Krasovskii functional, with a convex combination transformation, combining with the linear matrix inequalities(LMIs), we can get the feasibility conditions of the solution and the gain of controller. We mainly research four questions in this thesis:(1)Given the design of state feedback controller based on the sampled-data. Combining Lyapunov-Krasovskii functional, discusses the state of the sampling system of feedback controller design problem, analyze the sampling system status feedback system allows sufficient condition for stabilization, and through LMI feasibility of the solution, obtained sampling system status feedback stabilization gain matrix.(2)Given the observer design based on the output sampled-data and feedback stabilization. After discussing the observer output sample values based design, system reconfiguration through observer status and error conditions have been fully augmented feedback stabilization system and the feasibility of solving LMI system, and get feedback gain matrix K and the observer gain matrix L, and finally through Matlab simulation, combined the corresponding state curves and control curve, Through the analysis of these curve, it shows the feasibility of the method.(3)Given the stability analysis and control synthesis for nonlinear systems with variable sampling based on Takagi-Sugeno(T-S) fuzzy model approach. A novel piecewise Lyapunov-Krasovskii functional is constructed for stability analysis and controller design. Based on the feasibility of a set of linear matrix inequalities(LMIs), the sufficient conditions of stabilization via sampled-data feedback are proposed. Numerical example demonstrates the effectiveness of our results.(4)Given the output sampled-data observer design and feedback stabilization of nonlinear sample systems based on T-S fuzzy model. Based on the output sampled-data and the observer error, we construct fuzzy observer structure, and then design Lyapunov-Krasovskii functional with new created system variables. Through convex combination transform, combining free matrices variable, we get the stability conditions of the system. Solving LMIs feasibility conditions, we can get the sub-system’s feedback gain matrixiK and the observer gain matrixiL. Through the Matlab simulation, we get the rationality of the curve and the corresponding state control curve, which indicating the feasibility of the method.