L2-absolute and input-to-state stabilities of equations with nonlinear causal mappings

M. I. Gil

doi:10.1002/rnc.1305

L²-absolute and input-to-state stabilities of equations with nonlinear causal mappings

M. I. Gil

Department of Mathematics

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

8 Scopus citations

Abstract

Nonlinear scalar equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L ²-norms of solutions are established. These estimates give us explicit conditions for the absolute and input-to-state stabilities of the considered equations. The Aizerman-type problem from the theory of absolute stability is also discussed. The suggested approach enables us to consider various classes of systems from the unified point of view.

Original language	English
Pages (from-to)	151-167
Number of pages	17
Journal	International Journal of Robust and Nonlinear Control
Volume	19
Issue number	2
DOIs	https://doi.org/10.1002/rnc.1305
State	Published - 25 Jan 2009

Keywords

Absolute stability
Aizerman-type problem
Causal mappings
Difference equations with continuous time
Differential equations
Functional differential equations
Input-to-state stability

ASJC Scopus subject areas

Control and Systems Engineering
General Chemical Engineering
Biomedical Engineering
Aerospace Engineering
Mechanical Engineering
Industrial and Manufacturing Engineering
Electrical and Electronic Engineering

Access to Document

10.1002/rnc.1305

Cite this

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abstract = "Nonlinear scalar equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norms of solutions are established. These estimates give us explicit conditions for the absolute and input-to-state stabilities of the considered equations. The Aizerman-type problem from the theory of absolute stability is also discussed. The suggested approach enables us to consider various classes of systems from the unified point of view.",

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AB - Nonlinear scalar equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norms of solutions are established. These estimates give us explicit conditions for the absolute and input-to-state stabilities of the considered equations. The Aizerman-type problem from the theory of absolute stability is also discussed. The suggested approach enables us to consider various classes of systems from the unified point of view.

KW - Absolute stability

KW - Aizerman-type problem

KW - Causal mappings

KW - Difference equations with continuous time

KW - Differential equations

KW - Functional differential equations

KW - Input-to-state stability

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