000 03889nam a22004695i 4500
001 978-3-0348-0577-3
003 DE-He213
005 20140220082836.0
007 cr nn 008mamaa
008 130217s2013 sz | s |||| 0|eng d
020 _a9783034805773
_9978-3-0348-0577-3
024 7 _a10.1007/978-3-0348-0577-3
_2doi
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.352
_223
100 1 _aGil’, Michael I.
_eauthor.
245 1 0 _aStability of Vector Differential Delay Equations
_h[electronic resource] /
_cby Michael I. Gil’.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2013.
300 _aX, 259 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aFrontiers in Mathematics,
_x1660-8046
505 0 _aPreface -- 1 Preliminaries -- 2 Some Results of the Matrix Theory -- 3 General Linear Systems -- 4 Time-invariant Linear Systems with Delay -- 5 Properties of Characteristic Values -- 6 Equations Close to Autonomous and Ordinary Differential Ones -- 7 Periodic Systems -- 8 Linear Equations with Oscillating Coefficients -- 9 Linear Equations with Slowly Varying Coefficients -- 10 Nonlinear Vector Equations -- 11 Scalar Nonlinear Equations -- 12 Forced Oscillations in Vector Semi-Linear Equations -- 13 Steady States of Differential Delay Equations -- 14 Multiplicative Representations of Solutions -- Appendix A. The General Form of Causal Operators -- Appendix B. Infinite Block Matrices -- Bibliography -- Index.    .
520 _aDifferential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states.     The main methodology presented in the book is based on a combined usage of the recent norm estimates for matrix-valued functions and the following methods and results: the generalized Bohl-Perron principle and the integral version of the generalized Bohl-Perron principle; the freezing method; the positivity of fundamental solutions. A significant part of the book is devoted to  the Aizerman-Myshkis problem and  generalized Hill theory of periodic systems.     The book is intended not only for specialists in the theory of functional differential equations and control theory, but also for anyone with a sound mathematical background interested in their various applications.
650 0 _aMathematics.
650 0 _aDifferential Equations.
650 0 _aSystems theory.
650 1 4 _aMathematics.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aSystems Theory, Control.
650 2 4 _aApplications of Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034805766
830 0 _aFrontiers in Mathematics,
_x1660-8046
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0577-3
912 _aZDB-2-SMA
999 _c96309
_d96309