Finite-time Stability And Control Design Of Nonlinear Systems In Delayed Environment

The essence of finite-time stability(FTS)is a kind of performance estimation,which aims to study the transient performance of the system in the finite time domain.Whereas traditional Lyapunov stability is concerned with the behavior of a system over a sufficiently long(in principle infinite)time interval,FTS is a more applicable concept for studying the behavior of a system over a finite(possibly short)time interval,making it applicable to any desired state variable that does not exceed a given threshold(e.g.avoid saturation or nonlinear dynamic excitation)during transient processes.In addition,time delay is an inevitable phenomenon in many practical engineering and sciences,such as biology,neural networks,information technology,and manufacturing operations.Usually,this phenomenon exists in the system state,control input,or measurement process,and is often introduced as a delay system to be modeled in the above areas.In practice,delay systems often have complex dynamics and are the source of performance degradation or system instability.On the other hand,it can also make an unstable system stable or have the desired performance.Therefore,it is of great practical value to study the FTS of nonlinear systems in delay environment.This thesis establishes some conditions of FTS and finite-time contractive stability(FTCS)for nonlinear delay systems and nonlinear impulsive delay systems by using Lyapunov function technology,impulsive control theory and finite-time control analysis methods,and effective control strategies are put forward.The main content of this paper are included as follows:1.Based on the FTS,the concept of FTCS is further proposed for nonlinear delay systems,that is,the system is ”bounded” in finite time and has the property of ”contractive” in terminal time.By constructing LyapunovRazumikhin conditions of a class of integral functions,sufficient conditions for FTS and FTCS of delay systems are established.Then the theoretical results are applied to a class of linear time-varying delay systems.Finally,the effectiveness of the proposed criteria is verified by a class of ball motion models and memoryless control design of time-varying delay systems.2.The FTS and FTCS of a class of nonlinear systems involving statedependent delay are discussed.The state-dependent delay depends on system state which may change due to various factors,and then resulted in the uncertainty and unknown of the state-dependent delay.Considering two kinds of constraints of state-dependent delay,using Lyapunov function and some analysis methods tailed at the state-dependent delay,the criteria of FTS and FTCS of the system are given respectively.In addition,the theoretical results are applied to a class of nonlinear time-varying systems involving state-dependent delay.Finally,the effectiveness of the research results is verified by examples,in which the FTCS of submarine positioning system with state-dependent delay is considered,that is,the preset running time and required motion state of dynamic positioning system are quantitatively analyzed.3.The FTS analysis and control design for multiple impulsive delay systems are presented.A class of FTS-Lyapunov function is introduced,and combined with the impulsive control theory technique,the uniform FTS and uniform FTCS of the delay system under the class of impulse sequences are obtained.Furthermore,the stability criterion of a class of nonlinear impulsive systems based on LMIs is established by designing control input and constructing appropriate impulse sequences.Finally,the proposed method is validated by taking the automobile suspension system as a model.4.The FTS and FTCS of nonlinear systems including delay impulses are discussed.Considering the destabilizing impulses and stabilizing impulses respectively,the FTS-Lyapunov function based on delay impulses is constructed,and the delay impulse sequence which guarantees the uniform stability of the system is given.The relationship between the impulsive frequency and the time delay in the impulse is established without the constraint delay.As an application,we extend the theoretical results to the finite-time state estimation of neural networks,including time-varying neural networks and switched neural networks.Finally,two illustrated examples are given to show the effectiveness of the proposed delay-dependent impulsive schemes.