Stability Analysis And Controller Synthesis For Three Kinds Of Nonlinear Quadratic System

Quadratic systems are a special kind of nonlinear dynamic systems,which are widely existing in reality,such as electric and bioengineering,etc.Based on the existing studies,this dissertation provides several problems for analysis of stability of the quadratic system with time-delay,aims to obtain some new results.The full text is divided into four chapters:In Chapter 1,we introduce the research background of this article,the main task and some important preliminaries.In Chapter 2,in view of the nonlinear quadratic time-delay system,stability analysis and controller synthesis problems are studied.First of all,based on quadratic Lyapunov function and Razumikhin technique,sufficient conditions for LMI form the local stability is given.Secondly,the design method of nonlinear state feedback controller is given.Finally,simulation examples are provided to show the effectiveness of the proposed approach.In Chapter 3,in view of the nonlinear quadratic time-delay system for discrete-time with input saturation,stability analysis and control synthesis problems are studied.First of all,based on quadratic Lyapunov function,the LMI form of local stability criterion is given.Secondly,the design method of nonlinear state feedback controller is given.Finally,simulation examples are provided to show the effectiveness of the proposed approach.In Chapter 4,in view of the nonlinear quadratic time-delay system with input saturation,controller design problem is studied.Based on quadratic Lyapunov function and Razumikhin technique,the design method of linear state feedback controller is given.Simulation examples are provided to show the effectiveness of the proposed approach.