Quantized Stabilization of Two-Input Linear Systems: A Lower Bound on the Minimal Quantization Density

Authors:
Nicola Elia;Emilio Frazzoli
Affiliations:
-;-
Venue:
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Year:
2002

Citing 3
Cited 2

Elements of information theory

Elements of information theory
Qualitative modelling of linear dynamical systems with quantized state measurements

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Deterministic discrete-event representations of linear continuous-variable systems

Automatica (Journal of IFAC)

Brief paper: Multivariable quadratically-stabilizing quantizers with finite density

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Control and estimation under information constraints: Toward a unified theory of control, computation and communications

Automation and Remote Control

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Abstract

In this paper we derive a lower bound on the density of the coarsest quantizer that quadratically stabilizes a two-input linear discrete time system. This result describes how much improvement could be expected in terms of reduced quantization density by using two inputs instead of one to quadratically stabilize the system. A by-product result is that the optimal quantizer is radially logarithmic. This is a generalization of the logarithmic quantizer obtained in previous work.