L2-instability of vector equations with nonlinear causal mappings

M. I. Gil'

L²-instability of vector equations with nonlinear causal mappings

M. I. Gil'

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L ²-norm of solutions are established. The obtained estimates give us explicit conditions for the L²-stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.

Original language	English
Pages (from-to)	201-219
Number of pages	19
Journal	Dynamic Systems and Applications
Volume	17
Issue number	1
State	Published - 1 Mar 2008

Keywords

Absolute stability
Causal mappings
Difference equations with continuous time
Differential delay equations
Differential equations
Input-to-state stability
L-stability

ASJC Scopus subject areas

General Mathematics

Cite this

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abstract = "Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norm of solutions are established. The obtained estimates give us explicit conditions for the L2-stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.",

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N2 - Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norm of solutions are established. The obtained estimates give us explicit conditions for the L2-stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.

AB - Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norm of solutions are established. The obtained estimates give us explicit conditions for the L2-stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.

KW - Absolute stability

KW - Causal mappings

KW - Difference equations with continuous time

KW - Differential delay equations

KW - Differential equations

KW - Input-to-state stability

KW - L-stability

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M3 - Article

AN - SCOPUS:48949085093

SN - 1056-2176

VL - 17

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JO - Dynamic Systems and Applications

JF - Dynamic Systems and Applications

IS - 1

ER -

L²-instability of vector equations with nonlinear causal mappings

Abstract

Keywords

ASJC Scopus subject areas

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