Quantized stabilization of two-input linear systems: A lower bound on the minimal quantization density

Nicola Elia; Emilio Frazzoli

doi:10.1007/3-540-45873-5_16

Quantized stabilization of two-input linear systems: A lower bound on the minimal quantization density

Nicola Elia, Emilio Frazzoli

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

18 Scopus citations

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.

Original language	English (US)
Title of host publication	Hybrid Systems
Subtitle of host publication	Computation and Control - 5th International Workshop, HSCC 2002, Proceedings
Editors	Claire J. Tomlin, Mark R. Greenstreet
Publisher	Springer Verlag
Pages	179-193
Number of pages	15
ISBN (Print)	354043321X, 9783540433217
DOIs	https://doi.org/10.1007/3-540-45873-5_16
State	Published - Jan 1 2002
Externally published	Yes
Event	5th International Workshop on Hybrid Systems: Computation and Control, HSCC 2002 - Stanford, United States Duration: Mar 25 2002 → Mar 27 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2289
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	5th International Workshop on Hybrid Systems: Computation and Control, HSCC 2002
Country	United States
City	Stanford
Period	3/25/02 → 3/27/02

Access

10.1007/3-540-45873-5_16

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Cite this

Elia, N., & Frazzoli, E. (2002). Quantized stabilization of two-input linear systems: A lower bound on the minimal quantization density. In C. J. Tomlin, & M. R. Greenstreet (Eds.), Hybrid Systems: Computation and Control - 5th International Workshop, HSCC 2002, Proceedings (pp. 179-193). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2289). Springer Verlag. https://doi.org/10.1007/3-540-45873-5_16

Quantized stabilization of two-input linear systems : A lower bound on the minimal quantization density. / Elia, Nicola; Frazzoli, Emilio.

Hybrid Systems: Computation and Control - 5th International Workshop, HSCC 2002, Proceedings. ed. / Claire J. Tomlin; Mark R. Greenstreet. Springer Verlag, 2002. p. 179-193 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2289).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Elia, N & Frazzoli, E 2002, Quantized stabilization of two-input linear systems: A lower bound on the minimal quantization density. in CJ Tomlin & MR Greenstreet (eds), Hybrid Systems: Computation and Control - 5th International Workshop, HSCC 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2289, Springer Verlag, pp. 179-193, 5th International Workshop on Hybrid Systems: Computation and Control, HSCC 2002, Stanford, United States, 3/25/02. https://doi.org/10.1007/3-540-45873-5_16

Elia N, Frazzoli E. Quantized stabilization of two-input linear systems: A lower bound on the minimal quantization density. In Tomlin CJ, Greenstreet MR, editors, Hybrid Systems: Computation and Control - 5th International Workshop, HSCC 2002, Proceedings. Springer Verlag. 2002. p. 179-193. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45873-5_16

Elia, Nicola ; Frazzoli, Emilio. / Quantized stabilization of two-input linear systems : A lower bound on the minimal quantization density. Hybrid Systems: Computation and Control - 5th International Workshop, HSCC 2002, Proceedings. editor / Claire J. Tomlin ; Mark R. Greenstreet. Springer Verlag, 2002. pp. 179-193 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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