Stability Theory for Dynamic Equations on Time Scales. 1st ed. 2016

種類:

電子ブック

責任表示:

by Anatoly A. Martynyuk

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016

著者名:

• Martynyuk, Anatoly A.
• SpringerLink (Online service)

シリーズ名:

Systems & Control: Foundations & Applications ;

ISBN:

9783319422138 [3319422138]    

注記:

Contents -- Preface -- 1 Elements of Time Scales Analysis -- 2 Method of Dynamic Integral Inequalities -- 3 Lyapunov Theory for Dynamic Equations -- 4 Comparison Method -- 5 Applications -- References.
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 Math

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