Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.

[1]  Allan R. Willms,et al.  Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft , 1996 .

[2]  祁伟,et al.  Controlling a time-delay system using multiple delay feedback control , 2007 .

[3]  Xinzhi Liu,et al.  Uniform asymptotic stability of impulsive delay differential equations , 2001 .

[4]  Xinzhi Liu,et al.  Stability of impulsive control systems with time delay , 2004 .

[5]  Daniel W. C. Ho,et al.  Stability of Takagi–Sugeno Fuzzy Delay Systems With Impulse , 2007, IEEE Transactions on Fuzzy Systems.

[6]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[7]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[8]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[9]  L. Yang,et al.  Impulsive control for synchronization of nonlinear Rössler chaotic systems , 2006 .

[10]  Zhi-Hong Guan,et al.  Robust decentralized stabilization for a class of large-scale time-delay uncertain impulsive dynamical systems , 2002, Autom..

[11]  C. Wen,et al.  Switched and Impulsive Systems: Analysis, Design, and Applications , 2005, IEEE Transactions on Automatic Control.

[12]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[13]  Zhiguo Luo,et al.  New Razumikhin type theorems for impulsive functional differential equations , 2002, Appl. Math. Comput..

[14]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[15]  Qidi Wu,et al.  Impulsive control of a financial model , 2005 .

[16]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

[17]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[18]  Shao Shi-quan,et al.  Impulsive control of chaotic systems with exogenous perturbations , 2007 .

[19]  Tao Yang,et al.  Impulsive Systems and Control: Theory and Applications , 2001 .

[20]  Yu Zhang,et al.  Stability of impulsive linear differential equations with time delay , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[21]  吴炜,et al.  Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays , 2007 .

[22]  张荣,et al.  Impulsive generalized synchronization of chaotic system , 2007 .

[23]  Katrin Rohlf,et al.  Impulsive control of a Lotka-Volterra system , 1998 .

[24]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[25]  Ivanka M. Stamova,et al.  Lyapunov—Razumikhin method for impulsive functional differential equations and applications to the population dynamics , 2001 .

[26]  Magdi S. Mahmoud,et al.  New results on delay-dependent control of time-delay systems , 2005, IEEE Transactions on Automatic Control.

[27]  Zhengguo Li,et al.  Analysis and design of impulsive control systems , 2001, IEEE Trans. Autom. Control..

[28]  Jitao Sun,et al.  Boundedness of the solutions of impulsive differential systems with time-varying delay , 2004, Appl. Math. Comput..

[29]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[30]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.