A Subspace Intersection Based Method for Faster Computation of the Storage Function for the Lossless and All-Pass Cases

Ashish Kothyari; Cornelis Praagman; Madhu N. Belur; Debasattam Pal

A Subspace Intersection Based Method for Faster Computation of the Storage Function for the Lossless and All-Pass Cases

Ashish Kothyari, Cornelis Praagman, Madhu N. Belur, Debasattam Pal

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

The Algebraic Riccati Equation (ARE) cannot be formulated for the conservative/lossless and allpass cases, though the notion of `storage function' is well-defined for these cases too. New properties have been formulated recently about the storage function matrix for this case, which gave rise to new computational procedures. This paper targets improvement of this algorithm by avoiding some key computation intensive steps in minimal polynomial basis computation. We use the Zassenhaus method for basis computation for the sum and intersection of two subspaces. In addition to the conventional Zassenhaus method, for improved numerical accuracy, we propose LU and QR factorization methods with pivoting and compare the results.

Original language	English
Title of host publication	Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems
Pages	613-619
Number of pages	7
ISBN (Electronic)	978-1-5323-1358-5
Publication status	Published - 2016
Event	22nd International Symposium on the Mathematical Theory of Networks and Systems - Minneapolis, MN, United States Duration: 12-Jul-2016 → 15-Jul-2016

Conference

Conference	22nd International Symposium on the Mathematical Theory of Networks and Systems
Country/Territory	United States
City	Minneapolis, MN
Period	12/07/2016 → 15/07/2016

Keywords

s: Computational Control, Computations in Systems Theory, Optimal Contro

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@inproceedings{e414d5ed6c994ea587c75da5a91b57d0,

title = "A Subspace Intersection Based Method for Faster Computation of the Storage Function for the Lossless and All-Pass Cases",

abstract = "The Algebraic Riccati Equation (ARE) cannot be formulated for the conservative/lossless and allpass cases, though the notion of `storage function' is well-defined for these cases too. New properties have been formulated recently about the storage function matrix for this case, which gave rise to new computational procedures. This paper targets improvement of this algorithm by avoiding some key computation intensive steps in minimal polynomial basis computation. We use the Zassenhaus method for basis computation for the sum and intersection of two subspaces. In addition to the conventional Zassenhaus method, for improved numerical accuracy, we propose LU and QR factorization methods with pivoting and compare the results.",

keywords = "s: Computational Control, Computations in Systems Theory, Optimal Contro",

author = "Ashish Kothyari and Cornelis Praagman and Belur, {Madhu N.} and Debasattam Pal",

year = "2016",

language = "English",

pages = "613--619",

booktitle = "Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems",

note = "22nd International Symposium on the Mathematical Theory of Networks and Systems ; Conference date: 12-07-2016 Through 15-07-2016",

}

Kothyari, A, Praagman, C, Belur, MN & Pal, D 2016, A Subspace Intersection Based Method for Faster Computation of the Storage Function for the Lossless and All-Pass Cases. in Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems., ThB06.2, pp. 613-619, 22nd International Symposium on the Mathematical Theory of Networks and Systems, Minneapolis, MN, United States, 12/07/2016. <http://hdl.handle.net/11299/181518>

A Subspace Intersection Based Method for Faster Computation of the Storage Function for the Lossless and All-Pass Cases. / Kothyari, Ashish; Praagman, Cornelis; Belur, Madhu N. et al.
Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems. 2016. p. 613-619 ThB06.2.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - A Subspace Intersection Based Method for Faster Computation of the Storage Function for the Lossless and All-Pass Cases

AU - Kothyari, Ashish

AU - Praagman, Cornelis

AU - Belur, Madhu N.

AU - Pal, Debasattam

PY - 2016

Y1 - 2016

N2 - The Algebraic Riccati Equation (ARE) cannot be formulated for the conservative/lossless and allpass cases, though the notion of `storage function' is well-defined for these cases too. New properties have been formulated recently about the storage function matrix for this case, which gave rise to new computational procedures. This paper targets improvement of this algorithm by avoiding some key computation intensive steps in minimal polynomial basis computation. We use the Zassenhaus method for basis computation for the sum and intersection of two subspaces. In addition to the conventional Zassenhaus method, for improved numerical accuracy, we propose LU and QR factorization methods with pivoting and compare the results.

AB - The Algebraic Riccati Equation (ARE) cannot be formulated for the conservative/lossless and allpass cases, though the notion of `storage function' is well-defined for these cases too. New properties have been formulated recently about the storage function matrix for this case, which gave rise to new computational procedures. This paper targets improvement of this algorithm by avoiding some key computation intensive steps in minimal polynomial basis computation. We use the Zassenhaus method for basis computation for the sum and intersection of two subspaces. In addition to the conventional Zassenhaus method, for improved numerical accuracy, we propose LU and QR factorization methods with pivoting and compare the results.

KW - s: Computational Control, Computations in Systems Theory, Optimal Contro

M3 - Conference contribution

SP - 613

EP - 619

BT - Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems

T2 - 22nd International Symposium on the Mathematical Theory of Networks and Systems

Y2 - 12 July 2016 through 15 July 2016

ER -

A Subspace Intersection Based Method for Faster Computation of the Storage Function for the Lossless and All-Pass Cases

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