An Invariance Principle for Nonlinear Discrete Autonomous Dynamical Systems

@article{Alberto2007AnIP,
  title={An Invariance Principle for Nonlinear Discrete Autonomous Dynamical Systems},
  author={Lu{\'i}s F. C. Alberto and Ta{\'i}s R. Calliero and Andre C. P. Martins},
  journal={IEEE Transactions on Automatic Control},
  year={2007},
  volume={52},
  pages={692-697}
}
This note proposes an extension of LaSalle's invariance principle for nonlinear discrete autonomous dynamical systems. The invariance principle is extended to allow the first difference of the auxiliar scalar function (usually a Lyapunov function) to be positive in some bounded regions. Moreover, a uniform version is proposed to deal with nonlinear discrete dynamical systems that vary with parameters. Both extensions have the original invariance principle as a particular case. As a consequence… CONTINUE READING

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