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Ivan V. Gaishun The Introduction to the Theory of Linear Nonstationary Systems Minsk. 1999. 409 pages.
In Russian. Hardcover Published by The Institute of Mathematics of the NAS of Belarus, Minsk, Belarus.
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In the monograph, the systematic statement of the basic items of the theory of linear systems of differential equations with variable coefficients are given, at that are investigated as free systems (in which there are no entrance influences), and systems influenced by managing parameters. The brief information from the general theory of linear systems (existence of solutions, elements of stability problem, etc.) are given. On the basis of the concept of reducibility to the stationary form relatively to abstract group of linear transformations, from the unique point of view the Lyapynov-reducible systems, systems with periodic coefficients, proper systems, systems reducible with respect to groups of almost periodic, polynomial and orthogonal transformations are investigated. The completely, differential and uniform controllable and observable systems are investigated, the conditions of controllability and observability in the class of Chebyshev polynomials and generalized functions of finite order are received. The unimprovable in general conditions of reducibility of control (supervision) systems to initial forms -- scalar equations of the nth order (systems dual to them) -- with the help of various transformations groups are established. The application of the canonical forms to problems of stabilization, spectrum control, evaluation of the elements of motion, etc. is given. The problems of stability, controllability, observability and stabilization of nonlinear systems by the linear approximation are considered.
The book is aimed to the experts in the field of differential equations, mechanics and theory of control. It can be useful to the students of high schools trained in these topics.
Click here to read the Contents (in English or Russian) and Preface (in Russian).
Publisher's Mailing Address: 11 Surganava Street, Minsk BY-220072, Republic of Belarus
Telephone: +375 (17) 284-17-84. Fax: +375 (17) 284-09-15
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