Lyapunov functions. Barbashin E.A.

This book sets out a course of lectures on the method of Lyapunov’s functions, read by the author in the Belarusian Order of the Red Banner of Labor University named after V.I. Lenin (now Belarusian State University). The main attention is paid to the methods of building Lyapunov's functions for nonlinear systems. Methods of assessing the area of ​​attraction, assessment of decisions, regulation time, integrated criteria for the quality of regulation are given. Sufficient criteria for asymptotic stability in general, criteria of absolute stability are presented. A large number of Lyapunov functions are given for nonlinear systems of the second and third orders. The case is considered when non -linearity depends on two coordinates of the phase space points. The problem of building Lyapunov vector functions for complex systems is also investigated.

To understand the material, knowledge of the course of mathematics in the volume of the program of technical universities is necessary.

The book can be recommended to all the stability theory of sustainability that are interested in specific applications. < /p>