Control system

Mathematics

Computer science

Quantum mechanics

Machine learning

Engineering

Control (management)

Stability (learning theory)

Artificial intelligence

Exponential stability

Control theory (sociology)

Group delay and phase delay

Impulse (physics)

Electrical engineering

Physics

Nonlinear system

Bandwidth (computing)

Computer network

IEEE Transactions on Automatic Control

In this article, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive time-delay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive...

Potential Impacts of Delay on Stability of Impulsive Control Systems