Finite-gain \(L_\infty\) stability from disturbance to output of impulsive systems with time delay

Volume 10, Issue 4, pp 1593--1602 http://dx.doi.org/10.22436/jnsa.010.04.25

Publication Date: April 20, 2017 Submission Date: July 11, 2016

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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.

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Keywords

• Impulsive control
• impulsive disturbance
• Lyapunov function
• finite-gain \(L_\infty\) stability.

MSC

•  34A37
•  34C11

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