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By Anatoly A. Martynyuk

This monograph is a primary on the earth to give 3 ways for balance research of recommendations of dynamic equations. the 1st technique relies at the program of dynamic vital inequalities and the elemental matrix of strategies of linear approximation of dynamic equations. the second one is predicated at the generalization of the direct Lyapunovs procedure for equations on time scales, utilizing scalar, vector and matrix-valued auxiliary features. The 3rd strategy is the appliance of auxiliary features (scalar, vector, or matrix-valued ones) together with differential dynamic inequalities. this is often an alternate comparability technique, built for time non-stop and time discrete systems.
In fresh a long time, automated regulate thought within the examine of air- and spacecraft dynamics and in different parts of contemporary utilized arithmetic has encountered difficulties within the research of the habit of strategies of time continuous-discrete linear and/or nonlinear equations of perturbed motion. 
In the e-book “Men of Mathematics,” 1937, E.T.Bell wrote: “A significant job of arithmetic this day is to harmonize the continual and the discrete, to incorporate them in a single entire arithmetic, and to get rid of obscurity from both.”
Mathematical research on time scales accomplishes precisely this. 
This study has capability purposes in such components as theoretical and utilized mechanics, neurodynamics, mathematical biology and finance between others.

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Stability Theory for Dynamic Equations on Time Scales (Systems & Control: Foundations & Applications) by Anatoly A. Martynyuk


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