Stability Theory for Dynamic Equations on Time Scales / by Anatoly A. Martynyuk
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | Cham : Springer International Publishing : Imprint: Birkhäuser |
| 出版年 | 2016 |
書誌詳細を非表示
| 書誌ID | OB01018629 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 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. License restrictions may limit access Summary: 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 |
| 著者標目 | *Martynyuk, Anatoly A SpringerLink (Online service) |
| 統一書名標目 | Systems & Control: Foundations & Applications, |
| 件 名 | LCSH:Mathematics LCSH:Dynamics LCSH:Ergodic theory LCSH:System theory FREE:Mathematics FREE:Dynamical Systems and Ergodic Theory FREE:Systems Theory, Control |
| 分 類 | LCC:QA313 DC23:515.39 DC23:515.48 |
| 巻冊次 | ISBN:9783319422138 RefWorks出力（各巻） print ; ISBN:9783319422121 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
| 所蔵情報へのリンク | Stability theory for dynamic equations on time scales / Anatoly A. Martynyuk |
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