The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.

Stability Analysis of Nonlinear Systems (Systems & Control: Foundations & Applications)

Lakshmikantham, Vangipuram

Martynyuk, Anatoly A.

Leela, Srinivasa

Reference

Birkhauser

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.

Stability Theory for Dynamic Equations on Time Scales (Systems & Control: Foundations & Applications)

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Books by Martynyuk, Anatoly A.

See the best price to sell, buy, or rent books by Martynyuk, Anatoly A.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Stability Analysis of Nonlinear Systems (Systems & Control: Foundations & Applications)

Stability Theory for Dynamic Equations on Time Scales (Systems & Control: Foundations & Applications)

Stability Analysis of Nonlinear Systems (Systems & Control: Foundations & Applications)

Stability Theory for Dynamic Equations on Time Scales (Systems & Control: Foundations & Applications)