Analysis For Finite-time Stability Of Systems With Proportional Delay

Time delay systems are often used to describe control systems,neural networks,missile systems and other practical problems.It is necessary to consider the dynamic behaviors of the finite-time systems by reason of limitations of equipment life span and other factors.Due to the controllability and predictability of proportional delay,proportional delay systems are often used to describe many practical problems in engineering fields such as cybernetics and electrodynamics.Therefore,it is of great theoretical and practical significance to study the finite-time stability of systems with proportional delay.At the same time,impulses often affect the dynamic behaviors of actual systems,and studying the dynamic behaviors of impulsive delay systems are more difficult than simply discussing the impact of time delay or impulses on system dynamics.Therefore,studying the finite-time stability of impulsive systems with proportional delay deserve our further attention.In chapter 1,we state the purpose and significance of this thesis,and introduce the relevant research status at home and abroad.In chapter 2,we employ Lyapunov-Razumikhin method,some criteria ensuring finite-time stability and finite-time contractive stability of the systems with proportional delay are derived,and as an application,some criteria are derived to guarantee that the finite-time contractive stability of a class of neural networks with proportional delay.At last,the validity of the theoretical results are finally tested by numerical examples.In chapter 3,we mainly investigate the finite-time stability of impulsive systems with proportional delay.By combining Lyapunov-Razumikhin method with average impulsive interval approach,and proposing a novel Razumikhin condition,we derive some criteria to ensure that the addressed impulsive pantograph systems are finite-time stable.Also,based on this Razumikhin condition,new Lyapunov-based conditions are obtained for the finite-time stability and the global power stability of nonlinear pantograph systems.Finally,serval numerical examples are given to explain the validity and feasibility of the theoretical results obtained.Finally,as the end of this thesis,the main research contents and corresponding innovation points are summarized,forward prospects for future research are also proposed.