Duality for Multidimensional Linear Systems with Homological Dimension $\leq 1$

SIAM Journal on Control and Optimization ◽

10.1137/19m1299190 ◽

2021 ◽

Vol 59 (1) ◽

pp. 417-433

Author(s):

Vakhtang Lomadze

Keyword(s):

Linear Systems ◽

Homological Dimension ◽

Multidimensional Linear

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Closure to “Discussion of ‘On Stability of Time-Varying Multidimensional Linear Systems’ ” [ASME J. Vibr. Acoust., 121, No. 4, pp. 509–511 (1999)]

Journal of Vibration and Acoustics ◽

10.1115/1.1306389 ◽

2000 ◽

Vol 122 (3) ◽

pp. 338-338

Author(s):

Jinn-Wen Wu

Keyword(s):

Linear Systems ◽

Time Varying ◽

Multidimensional Linear

[S0739-3717(00)00704-2]

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Discussion: “On Stability of Time-Varying Multidimensional Linear Systems” [ASME J. Vibr. Acoust., 121, No. 4, pp. 509–511 (1999)]1

Journal of Vibration and Acoustics ◽

10.1115/1.1305922 ◽

2000 ◽

Vol 122 (3) ◽

pp. 337-338 ◽

Author(s):

S. M. Shahruz

Keyword(s):

Linear Systems ◽

Time Varying ◽

Multidimensional Linear

[S0739-3717(00)00604-8]

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Robust and efficient quantization and coding for control of multidimensional linear systems under data rate constraints

International Journal of Robust and Nonlinear Control ◽

10.1002/rnc.1142 ◽

2007 ◽

Vol 17 (10-11) ◽

pp. 898-920 ◽

Author(s):

K. Li ◽

J. Baillieul

Keyword(s):

Linear Systems ◽

Data Rate ◽

Multidimensional Linear ◽

Rate Constraints

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APPLICATION OF LINEAR MATRIX INEQUALITIES DURING SYNTHESIS OF MODULAR CONTROL BY MULTIDIMENSIONAL LINEAR SYSTEMS

Scientific Works of National University of Food Technologies ◽

10.24263/2225-2924-2018-24-3-4 ◽

2018 ◽

Vol 24 (3) ◽

pp. 16-25

Author(s):

O. Lobok ◽

B. Goncharenko ◽

M. Sych

Keyword(s):

Linear Systems ◽

Linear Matrix Inequalities ◽

Linear Matrix ◽

Matrix Inequalities ◽

Modular Control ◽

Multidimensional Linear

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Robust quantization and coding for multidimensional linear systems under data rate constraints

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) ◽

10.1109/cdc.2004.1430328 ◽

2004 ◽

Author(s):

K. Li ◽

J. Baillieul

Keyword(s):

Linear Systems ◽

Data Rate ◽

Multidimensional Linear ◽

Rate Constraints

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Multidimensional linear systems: the extra term

42nd Midwest Symposium on Circuits and Systems (Cat. No.99CH36356) ◽

10.1109/mwscas.1999.867788 ◽

2003 ◽

Author(s):

I.W. Sandberg

Keyword(s):

Linear Systems ◽

Multidimensional Linear

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THE CAUCHY PROBLEM FOR MULTIDIMENSIONAL LINEAR SYSTEMS OVER GEVREY SPACES

Mathematics of the USSR-Sbornik ◽

10.1070/sm1969v008n02abeh001119 ◽

1969 ◽

Vol 8 (2) ◽

pp. 249-273

Author(s):

V A Sočneva ◽

V R Fridlender

Keyword(s):

Cauchy Problem ◽

Linear Systems ◽

Gevrey Spaces ◽

The Cauchy Problem ◽

Multidimensional Linear

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PARAMETRIZING ALL SOLUTIONS OF UNCONTROLLABLE MULTIDIMENSIONAL LINEAR SYSTEMS

IFAC Proceedings Volumes ◽

10.3182/20050703-6-cz-1902.00578 ◽

2005 ◽

Vol 38 (1) ◽

pp. 49-54 ◽

Author(s):

A. Quadrat ◽

D. Robertz

Keyword(s):

Linear Systems ◽

All Solutions ◽

Multidimensional Linear

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A constructive algebraic analysis approach to the equivalence of multidimensional linear systems

2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS) ◽

10.1109/nds.2015.7332634 ◽

2015 ◽

Author(s):

Thomas Cluzeau

Keyword(s):

Linear Systems ◽

Analysis Approach ◽

Algebraic Analysis ◽

Multidimensional Linear

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On Stability of Time-Varying Multidimensional Linear Systems

Journal of Vibration and Acoustics ◽

10.1115/1.2894012 ◽

1999 ◽

Vol 121 (4) ◽

pp. 509-511 ◽

Author(s):

Jinn-Wen Wu ◽

Rong-Fong Fung

Keyword(s):

Exponential Stability ◽

Linear Systems ◽

Stiffness Matrix ◽

Minimum Amount ◽

Sufficient Condition ◽

Time Varying ◽

Multidimensional Linear

In this Technical Brief, a sufficient condition to guarantee the exponential stability for a time-varying system X¨ + DX˙ + K(t)X = 0 is obtained. We mainly made up the condition by estimating the minimum amount of the damping to cope with a time-varying stiffness matrix K(t).

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