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Qualitative analysis of set-valued differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Qualitative analysis of set-valued differential equations/ by Anatoly A. Martynyuk.
Author:	Martynyuk, Anatoly A.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xiii, 198 p. :ill., digital ;24 cm.
[NT 15003449]:	General Properties of Set Equations -- Analysis of the Set of Continuous Equations -- Stability of the Set of Discrete-Time Systems -- Qualitative Analysis of Set Impulsive Equations -- Stability of Set Systems with Aftereﬀect -- Analysis of Set Impulsive Systems with Aftereﬀect -- Stability of Set Equations with Causal Operator -- Finite-Time Stability of Standard Systems Sets.
Contained By:	Springer eBooks
Subject:	Differential equations - Qualitative theory. -
Online resource:	https://doi.org/10.1007/978-3-030-07644-3
ISBN:	9783030076443

Qualitative analysis of set-valued differential equations
Martynyuk, Anatoly A.

Qualitative analysis of set-valued differential equations[electronic resource] /by Anatoly A. Martynyuk. - Cham :Springer International Publishing :2019. - xiii, 198 p. :ill., digital ;24 cm.

General Properties of Set Equations -- Analysis of the Set of Continuous Equations -- Stability of the Set of Discrete-Time Systems -- Qualitative Analysis of Set Impulsive Equations -- Stability of Set Systems with Aftereﬀect -- Analysis of Set Impulsive Systems with Aftereﬀect -- Stability of Set Equations with Causal Operator -- Finite-Time Stability of Standard Systems Sets.

The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin - Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the ﬁeld of qualitative analysis of differential and other types of equations.

ISBN: 9783030076443

Standard No.: 10.1007/978-3-030-07644-3doiSubjects--Topical Terms:

779001
Differential equations
--Qualitative theory.

LC Class. No.: QA371

Dewey Class. No.: 515.35

Qualitative analysis of set-valued differential equations
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100 1 $a Martynyuk, Anatoly A. $3 2165657
245 1 0 $a Qualitative analysis of set-valued differential equations $h [electronic resource] / $c by Anatoly A. Martynyuk.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xiii, 198 p. : $b ill., digital ; $c 24 cm.
505 0 $a General Properties of Set Equations -- Analysis of the Set of Continuous Equations -- Stability of the Set of Discrete-Time Systems -- Qualitative Analysis of Set Impulsive Equations -- Stability of Set Systems with Aftereﬀect -- Analysis of Set Impulsive Systems with Aftereﬀect -- Stability of Set Equations with Causal Operator -- Finite-Time Stability of Standard Systems Sets.
520 $a The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin - Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the ﬁeld of qualitative analysis of differential and other types of equations.
650 0 $a Differential equations $x Qualitative theory. $3 779001
650 1 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Systems Theory, Control. $3 893834
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-07644-3
950 $a Mathematics and Statistics (Springer-11649)