Input-to-State Stability of Nonlinear Impulsive Systems

@article{Dashkovskiy2013InputtoStateSO,
  title={Input-to-State Stability of Nonlinear Impulsive Systems},
  author={Sergey Dashkovskiy and Andrii Mironchenko},
  journal={SIAM J. Control and Optimization},
  year={2013},
  volume={51},
  pages={1962-1987}
}
We prove that impulsive systems, which possess an input-to-state stable (ISS) Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition. If an ISS Lyapunov function is the exponential one, we provide a stronger result, which guarantees uniform ISS of the whole system over sequences satisfying the generalized average dwell-time condition. Then we prove two small-gain theorems that provide a construction of an ISS Lyapunov function for an interconnection of impulsive… CONTINUE READING
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