一类积分时滞系统的稳定性及鲁棒稳定性分析
发布时间：2018-11-18 12:48
【摘要】：在电子工程、医学和生物领域中,时滞问题普遍存在。为了更精确地刻画事物的运动规律,含有时滞的泛函微分方程得到了越来越多的研究。本文主要分析了一类积分时滞系统的稳定性及鲁棒稳定性,包括稳定性定理,指数稳定的充分条件以及数值求解方法,并探讨了其在中立型随机微分系统稳定性问题中的应用。首先,文章基于一般积分时滞系统的Lyapunov型稳定性定理,通过选择合适的Lyapunov函数,并运用不等式放缩技巧,建立了一类保证积分时滞系统稳定的基于线性矩阵不等式的充分条件。其次,分析了此类系统的鲁棒稳定性问题,通过对原有系统的不同项上施加扰动,讨论系统的鲁棒稳定性,同样构造了保证系统稳定的一类Lyapunov泛函的形式,进而给出了当有扰动作用时,系统的鲁棒稳定性定理,并给出了相应的证明。进而,本文给出了数值例子来验证所给出结论的实际应用性,针对充分条件,举出数值例子,求出系统稳定对应的时滞范围,从而验证本文已得出的结论的有效性。并与一些之前已有的结论做出对比来验证保守性。最后,作为积分时滞系统的一个应用,文章讨论了一类含有分布时滞和布朗运动的中立型随机微分方程的稳定性问题,此类系统的稳定性与前面讨论的积分时滞系统密切相关。利用积分时滞系统稳定的相关条件,建立了判断此类随机微分方程均方稳定的一组充分条件。
[Abstract]:In the fields of electronic engineering, medicine and biology, the problem of time delay is common. In order to describe the law of motion more and more accurately, functional differential equations with time delay have been studied more and more. In this paper, the stability and robust stability of a class of integro-delay systems are analyzed, including stability theorems, sufficient conditions for exponential stability and numerical solutions, and their applications to the stability problems of neutral stochastic differential systems are discussed. Firstly, based on the Lyapunov type stability theorem of general integral delay systems, by selecting appropriate Lyapunov functions and using the technique of inequality scaling, the sufficient conditions based on linear matrix inequalities (LMI) for the stability of integral delay systems are established. Secondly, the problem of robust stability of this kind of systems is analyzed. The robust stability of the system is discussed by perturbation on different terms of the original system, and a class of Lyapunov functional forms which guarantee the stability of the system are also constructed. Furthermore, the robust stability theorem for the system with perturbation is given, and the corresponding proof is given. Furthermore, a numerical example is given to verify the practical application of the proposed conclusion. For sufficient conditions, numerical examples are given to obtain the time-delay range corresponding to the stability of the system, thus validating the validity of the conclusions obtained in this paper. And compared with some previous conclusions to verify the conservatism. Finally, as an application of integral delay systems, this paper discusses the stability of a class of neutral stochastic differential equations with distributed delays and Brownian motions. The stability of such systems is closely related to the integral delay systems discussed previously. A set of sufficient conditions for judging the mean square stability of such stochastic differential equations are established by using the relative conditions for the stability of integro-delay systems.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O211.63
，
本文编号：2340077
[Abstract]:In the fields of electronic engineering, medicine and biology, the problem of time delay is common. In order to describe the law of motion more and more accurately, functional differential equations with time delay have been studied more and more. In this paper, the stability and robust stability of a class of integro-delay systems are analyzed, including stability theorems, sufficient conditions for exponential stability and numerical solutions, and their applications to the stability problems of neutral stochastic differential systems are discussed. Firstly, based on the Lyapunov type stability theorem of general integral delay systems, by selecting appropriate Lyapunov functions and using the technique of inequality scaling, the sufficient conditions based on linear matrix inequalities (LMI) for the stability of integral delay systems are established. Secondly, the problem of robust stability of this kind of systems is analyzed. The robust stability of the system is discussed by perturbation on different terms of the original system, and a class of Lyapunov functional forms which guarantee the stability of the system are also constructed. Furthermore, the robust stability theorem for the system with perturbation is given, and the corresponding proof is given. Furthermore, a numerical example is given to verify the practical application of the proposed conclusion. For sufficient conditions, numerical examples are given to obtain the time-delay range corresponding to the stability of the system, thus validating the validity of the conclusions obtained in this paper. And compared with some previous conclusions to verify the conservatism. Finally, as an application of integral delay systems, this paper discusses the stability of a class of neutral stochastic differential equations with distributed delays and Brownian motions. The stability of such systems is closely related to the integral delay systems discussed previously. A set of sufficient conditions for judging the mean square stability of such stochastic differential equations are established by using the relative conditions for the stability of integro-delay systems.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O211.63
，
本文编号：2340077
本文链接：https://www.wllwen.com/kejilunwen/yysx/2340077.html
