Introduction to the theory of stability. Barbashin E.A.

This book sets out a course of lectures on the theory of sustainability, read by the author at the Ural State University. A. M. Gorky. The first chapter is devoted to the Lyapunov functions method. A special place is given to the development of the theory of stability in any initial disturbances; Methods of building Lyapunov functions for nonlinear systems are also described. In the second chapter, methods of stabilization of systems are considered, the parameters of which can change widely; The issues of stability of systems with a variable structure are set out. The third chapter is devoted to the study of the stability of solutions of equations set in functional spaces. The achievements in this area are described, obtained by both the author of the book and other scientists. A special place is given to the issues of stability in impulse disturbances, the task of accumulating indignation, as well as issues of the theory of software regulation.

to understand the material of the book, it is necessary to know the course of mathematics in the volume of the program of technical universities. If it is necessary to attract a mathematical structure, going beyond the specified program, a full description of this design is given with reference to the source.

The book can be recommended to students, graduate students, scientists and engineers involved in applied mathematics issues and wanting to expand their knowledge on the theory of stability.