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 May 27, 2023

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.