Exponential Stability Analysis Of Neutral Time-delay Systems

An important research problem in dynamic system theory is the stability analysis of the system.The research on neutral time-delay systems is one of the hot spots in control field in recent decades.The system is not only related to the past movement states,also associated with the rate of change of the past motion state.Compared with retarded time-delay systems,neutral time-delay system is able to more accurately describe the dynamic law of things,so the study of the system can provide theoretical support for solving practical problems.This paper mainly proves the necessary conditions and sufficient and necessary conditions for the exponential stability of neutral time-delay systems.The main contents are as follows:The generation and development of neutral time-delay systems,research status and application value are summarized.The basic matrix of the system is defined,and the complete type Lyapunov-Krasovskii functional is constructed.The expression of the derivative of the functional along the solution of the system is derived,which leads to the concept of the Lyapunov matrix.When the system is exponentially stable,the quadratic lower bound of the complete type functional,the basic properties of the Lyapunov matrix,and the relationship between the Lyapunov matrix and the basic matrix are given.By defining a new bilinear functional,the necessary conditions for the exponential stability of the system are obtained.By theoretical comparison,it is proved that the delay-dependent necessary conditions are less conservative than the related results in the literature.Numerical examples show that the necessary conditions can be used to estimate the exact stability region.Finally,the concept of Lyapnov condition is introduced,which can guarantee the existence and uniqueness of Lyapunov matrix.On the basis of this,the necessary and sufficient conditions of exponential stability for the neutral type time-delay system is obtained.