Generalization of integral inequalities and (c_1,c_1) stability of neutral differential equations with time-varying delays  

作　　者：Shuli Guo Lina Han 

机构地区：[1]Key Laboratory of Complex System Intelligent Control and Decision, School of Automation, Beijing Institute of Technology [2]Mathematics Institute, Oxford University [3]Department of Cardiovascular Internal Medicine, Nanlou Branch of Chinese PLA General Hospital

出　　处：《Journal of Systems Engineering and Electronics》2017年第2期347-360,共14页系统工程与电子技术（英文版）

基　　金：supported by the National Natural Science Foundation of China(61370136);the Hainan Province Science and Technology Cooperation Fund Project(KJHZ2015-36);the Hainan Province Introduced and Integrated Demonstration Projects(YJJC20130009)

摘　　要：A uniform stability analysis is developed for a type of neutral delays differential equations which depend on more general nonlinear integral inequalities. Many original investigations and results are obtained. Firstly, generations of two integral nonlinear inequalities are presented, which are very effective in dealing with the complicated integro-differential inequalities whose variable exponents are greater than zero. Compared with existed integral inequalities, those proposed here can be applied to more complicated differential equations, such as time-varying delay neutral differential equations. Secondly, the notions of (ω, Ω) uniform stable and (ω, Ω) uniform asymptotically stable, especially (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable, are presented. Sufficient conditions on about (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable of time-varying delay neutral differential equations are established by the proposed integral inequalities. Finally, a complex numerical example is presented to illustrate the main results effectively. The above work allows to provide further applications on the proposed stability analysis and control system design for different nonlinear systems. © 2017 Beijing Institute of Aerospace Information.A uniform stability analysis is developed for a type of neutral delays differential equations which depend on more general nonlinear integral inequalities. Many original investigations and results are obtained. Firstly, generations of two integral nonlinear inequalities are presented, which are very effective in dealing with the complicated integro-differential inequalities whose variable exponents are greater than zero. Compared with existed integral inequalities, those proposed here can be applied to more complicated differential equations, such as time-varying delay neutral differential equations. Secondly, the notions of (ω, Ω) uniform stable and (ω, Ω) uniform asymptotically stable, especially (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable, are presented. Sufficient conditions on about (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable of time-varying delay neutral differential equations are established by the proposed integral inequalities. Finally, a complex numerical example is presented to illustrate the main results effectively. The above work allows to provide further applications on the proposed stability analysis and control system design for different nonlinear systems. © 2017 Beijing Institute of Aerospace Information.

关 键 词：Control system stability Differential equations Nonlinear equations Time delay Time varying control systems 

分 类 号：O175[理学—数学]