Introduction to stability theory

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, the methods of constructing Lipunov functions for nonlinear systems are also described. The second chapter discusses the methods of stabilizing systems, the parameters of which can change within a wide range, outlines the stability of systems with a variable structure. 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 sustainability issues in impulse disturbances, the task of accumulating disturbances, as well as issues of software regulation theory.
To understand the material of the book, knowledge of the course of mathematics in the volume of the program of technical universities is necessary. If it is necessary to attract a mathematical structure, which goes beyond the specified program, a complete 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 sustainability