Finite-gain \(L_\infty\) stability from disturbance to output of impulsive systems with time delay
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Authors
Ping Li
- School of Computer Science and Technology, Southwest Minzu University, Chengdu, 610041, P. R. China.
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Xinzhi Liu
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Wu Zhao
- School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China.
Abstract
This paper studies finite-gain \(L_\infty\) stability from disturbance to output of delayed impulsive systems. By employing the
method of Lyapunov function, several criteria of finite-gain \(L_\infty\) stability from disturbance to output are established. It shows
that the linear delayed differential systems can be finite-gain \(L_\infty\)stabilized from disturbance to output using impulsive feedback
control even there is unstable matrix. Moreover, delayed differential equations also may be finite-gain \(L_\infty\) stable from disturbance
to output under an appropriate sequence of impulses treated as disturbances. Two examples and their simulations are also given
to illustrate our results.
Share and Cite
ISRP Style
Ping Li, Xinzhi Liu, Wu Zhao, Finite-gain \(L_\infty\) stability from disturbance to output of impulsive systems with time delay, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1593--1602
AMA Style
Li Ping, Liu Xinzhi, Zhao Wu, Finite-gain \(L_\infty\) stability from disturbance to output of impulsive systems with time delay. J. Nonlinear Sci. Appl. (2017); 10(4):1593--1602
Chicago/Turabian Style
Li, Ping, Liu, Xinzhi, Zhao, Wu. "Finite-gain \(L_\infty\) stability from disturbance to output of impulsive systems with time delay." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1593--1602
Keywords
- Impulsive control
- impulsive disturbance
- Lyapunov function
- finite-gain \(L_\infty\) stability.
MSC
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