Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 54, Issue 4, Pages 871-875Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2008.2010968
Keywords
Discrete system; impulsive control; Lyapunov functional; Razumikhin technique; stability; time delay
Funding
- National Natural Science Foundation of China [60874027]
- Program for Young Excellent Talents in Tongji University [2007KJ007]
- Research Grants Council of the Hong Kong Special Administrative Region, China [112907]
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This note deals with impulsive control of discrete systems with time delay. It's the first time that an impulsive controller was introduced for discrete systems with time delay. Firstly, some stability criteria for delay discrete systems with impulse effects are obtained by using Lyapunov functionals and Razumikhin technique. These stability criteria show that if the impulses satisfy some conditions, then the original stable systems can keep their stability property even with impulse effects. Then by using Lyapunov functionals or Lyapunov functions together with Razumikhin technique, two stability criteria for the discrete systems with time delay under impulsive control are given. These two results show that unstable systems can be stable under impulsive control. Some examples are also presented to illustrate the efficiency of the obtained results.
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