Abstract
This chapter discusses the linearization of the equations and A. M. Liapunov's theorem on the stability of linearized systems. The linear equations of real automatic systems are always obtained as a result of some linearization, that is, as a result of dropping terms containing the second and higher powers of the deviations of the variable and their derivatives. A. M. Liapunov gave many theorems and methods for investigating stability and the general behavior of dynamic systems in various cases that are difficult to analyze by normal methods. The best known are his methods for studying nonlinear systems. The chapter discusses the types of elements in automatic systems and their characteristics. The types of elements in automatic regulation systems, independently of their design and physical nature, are distinguished by their dynamic properties, that is, by the form of the differential equation of motion, which is most important for the theory of regulation and for technical calculation of closed automatic systems.
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