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Nonlinear stabilization by hybrid quantized feedback. (English) Zbl 0952.93109

Lynch, Nancy (ed.) et al., Hybrid systems: computation and control. 3rd international workshop, HSCC 2000, Pittsburgh, PA, USA, March 23-25, 2000. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1790, 243-257 (2000).
A quantizer is a piecewise constant function defined by \[ q_\Delta(x)= \begin{cases} k\Delta, &(k-1/2) \Delta\leq x< (k+1/2)\Delta, \quad k\in{\mathcal I},\\ M\Delta, &x\geq (M+1/2) \Delta,\\ -M\Delta, &x\leq -(M+1/2) \Delta. \end{cases} \] For the controlled system \[ \dot x= Ax+Bu \] the hybrid quantized feedback \(u= q_\Delta(x)\) is considered; its stabilizing properties are analyzed via a quadratic Lyapunov function. Further the nonlinear case \[ \dot x= f(x,k(x+e)) \] is considered, where \(k(x)\) is the feedback law and \(e\) is the quantization error. The input-to-state (ISS) stability is considered and applied to this system.
For the entire collection see [Zbl 0934.00029].

MSC:

93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
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