Stability Analysis And Control Of Singularly Perturbed Lurie Systems With Time-Varying Delay

With the rapid development of science and technology,people constantly improve the cognitive ability,by the complete development in-depth field of control the researchers have to study more complex nonlinear systems.Lurie system which can more accurately model and reflect the objective reality is a kind of nonlinear system with typical structure characteristics and wide application background.It represents many essential characteristics of nonlinear systems.The system is a form feedback system,the feedforward channel and feedback channel are the linear time-invariant system and the nonlinear segment satisfied the fan-shaped constraint.In fact,we can isolate nonlinear parts of nonlinear systems by nonlinear isolation to construct the Lurie systems.Therefore,it is of great significance to further improve the system theory and to research the essential characteristics of it.In the practical life,because of its complexity,the analysis and synthesis of the Lurie systems under the condition of time-varying delay,perturbation and uncertainty had always been a hot issue in the field of control theory and control engineering.At present,there is very few literatures on it in the current research results.So it is very necessary to study the analysis and control of the singularly perturbed Lurie systems with uncertain time-varying delay.Based on the existing literatures,stability analysis and controller design theory,in this paper,the absolute stability analysis and stabilization of Lurie systems with time-varying delay uncertainty are studied.The main results are generalized as follows:Firstly,the research results of the Lurie systems in recent decades are introduced.Several methods for the stability with the current research Lurie systems are summarized.To explain the main purpose and content of this article Including preliminary knowledge overviewed Luire systems theory,linear systems,nonlinear systems and absolute stability.Secondly,the stability of the singularly perturbed Lurie systems with uncertain time-varying delay is analyzed in two sector regions by selecting a new Lyapunov functional: [0,V] and [V₁,V₂].At the same time,the new stability criterion and the simplicity corollaries of time-delay dependent and time-delay independent are introduced.Thirdly,owing to the characteristics of the Lurie systems,feedback controllers are designed for the singularly perturbed Lurie systems with uncertain time-varying delay in the sector region [V₁,V₂],after that the state feedback control law is deduced.Finally,the feasibility and superiority are illustrated by numerical examples.