Subtleties in Robust Stability of Discrete-time Piecewise Affine Systems

@article{Lazar2007SubtletiesIR,
  title={Subtleties in Robust Stability of Discrete-time Piecewise Affine Systems},
  author={Mircea Lazar and W. P. Maurice H. Heemels and A. R. Teel},
  journal={2007 American Control Conference},
  year={2007},
  pages={3464-3469}
}
In this paper we consider (inherent) robustness of discrete-time piecewise affine (PWA) systems. We demonstrate, via examples, that globally exponentially stable discrete-time PWA systems may have no robustness. More precisely, we show that the exponential stability property cannot prevent that arbitrarily small additive disturbances keep the state trajectory far from the origin. Mathematically speaking, this means that the system is not input-to-state stable with respect to arbitrarily small… CONTINUE READING