Stability Theory for Dynamic Equations on Time Scales

Anatoly A. Martynyuk


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This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.
In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. 
In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”
Mathematical analysis on time scales accomplishes exactly this. 

This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

Détails
Auteur
Anatoly A.  Martynyuk
Marque
Birkhäuser
Collection
Systems & Control: Foundations & Applications
Parution
2016-09-22
Pages
223 pages
EAN papier
9783319422121
Langue
Anglais
Informations ebook
EAN PDF
9783319422138
Prix
51,04 €
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Nb pages copiables 2
Nb pages imprimables 22
Taille du fichier 2058 Ko
Ce livre est accessible aux handicaps   Informations sur l'accessibilité
EAN EPUB
9783319422138
Prix
51,04 €
En savoir plus
Nb pages copiables 2
Nb pages imprimables 22
Taille du fichier 3441 Ko
Ce livre est accessible aux handicaps   Informations sur l'accessibilité
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Defaut-Illustration Anatoly A. Martynyuk
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