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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Stability Theory for Dynamic Equations on Time Scales (Hardcover, 1st ed. 2016)
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Stability Theory for Dynamic Equations on Time Scales (Hardcover, 1st ed. 2016)
Series: Systems & Control: Foundations & Applications
Expected to ship within 12 - 17 working days
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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.
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