Nonlinear small-gain theorems for discrete-time feedback systems and applications

@article{Jiang2004NonlinearST,
  title={Nonlinear small-gain theorems for discrete-time feedback systems and applications},
  author={Zhong-Ping Jiang and Yuandan Lin and Yuan Xu Wang},
  journal={Automatica},
  year={2004},
  volume={40},
  pages={2129-2136}
}
We derive in this work a local nonlinear small-gain theorem in the framework of input-to-state stability for discrete time systems. Our primary objective is to show that, as in the continuous-time context, these discrete-time nonlinear small-gain theorems are very effective in stability analysis and synthesis for various classes of discrete-time control systems. Two converse Lyapunov theorems for discrete exponential stability are developed to assist these applications. New results in stability… CONTINUE READING
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