Abstract
The chapter deals with the investigation of nonlinear systems stability, a characteristic exponent and asymptotic stability. It also deals with the Lyapunov transformation to carry out a linear system whose matrix elements are functions of a system with a constant matrix. The examination of different methods for the construction of Lyapunov functions of nonlinear systems. The stability of systems with changeable parameters as well as the application of nonlinear systems control theory to the problems of artificial pneumatic muscle - APM control have also been investigated in the chapter.
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