COMPUTING RANK-DEFICIENCY OF RECTANGULAR MATRIX PENCILS.

D. L. Boley

doi:10.1109/cdc.1986.267365

COMPUTING RANK-DEFICIENCY OF RECTANGULAR MATRIX PENCILS.

D. L. Boley

Computer Science and Engineering

Research output: Contribution to journal › Conference article › peer-review

Abstract

Computing whether a system is close to uncontrollable is numerically difficult task. Some preliminary results on a simple experimental approach are presented. The method is based on reducing the problem to a rank problem for a certain matrix pencil. This method exhibits locally quadratic convergence to a local minimum of a function that yields the distance (in the state-space sense) to the nearest uncontrollable system from a given system. The entire computation take place in state space for numerical stability. This algorithm is used to compute the distance for certain examples, and the examples are used to show some severe limitations on the popular staircase algorithm.

Original language	English (US)
Pages (from-to)	554-557
Number of pages	4
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/cdc.1986.267365
State	Published - 1986

Bibliographical note

Funding Information:
* This research was partially supported by NSF Grants DCR-8420935 and DCR-8519029.

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title = "COMPUTING RANK-DEFICIENCY OF RECTANGULAR MATRIX PENCILS.",

abstract = "Computing whether a system is close to uncontrollable is numerically difficult task. Some preliminary results on a simple experimental approach are presented. The method is based on reducing the problem to a rank problem for a certain matrix pencil. This method exhibits locally quadratic convergence to a local minimum of a function that yields the distance (in the state-space sense) to the nearest uncontrollable system from a given system. The entire computation take place in state space for numerical stability. This algorithm is used to compute the distance for certain examples, and the examples are used to show some severe limitations on the popular staircase algorithm.",

author = "Boley, {D. L.}",

note = "Funding Information: * This research was partially supported by NSF Grants DCR-8420935 and DCR-8519029.",

year = "1986",

doi = "10.1109/cdc.1986.267365",

language = "English (US)",

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journal = "Proceedings of the IEEE Conference on Decision and Control",

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COMPUTING RANK-DEFICIENCY OF RECTANGULAR MATRIX PENCILS.

Abstract

Bibliographical note

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