17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper TuP08.2

Martins, Nuno C. (Univ. of Maryland)

Finite Gain L_p Stabilization Is Impossible under Finite Data-Rate Control

Scheduled for presentation during the Mini-Symposium "Networked control: Rate constraints and quantization effects" (TuP08), Tuesday, July 25, 2006, 15:45−16:10, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on June 23, 2024

Keywords Networked control, Stability analyisis, Quantization

Abstract

In this paper, we show that the finite gain (FG) l_p stabilization of a discrete-time, linear and time-invariant unstable plant cannot be achieved using a finite data-rate control law. We establish a comparison with existing work, leading to two conclusions: (1) in spite of ISS stability being attainable under data rate constrained feedback, small changes in the amplitude of the external excitation may cause, in relative terms, a large increase in the amplitude of the state (2) FG l_p stabilization requires logarithmic precision around zero, implying that even without data-rate constraints FG l_p stabilization is impossible in practice. Since our conclusions hold with no assumptions on the feedback structure, they cannot be derived from existing results.