ABSTRACT
The analysis of the asymptotic systems was pioneered by A. M. Lyapunov in his theses that was published almost 100 years ago [1]. Lyapunov’s method is not only a basic tool in the analysis of system stability but also a very valuable tool for the synthesis of controllers for nonlinear systems. Lyapunov divided the problem of stability analysis of nonlinear systems into two groups. The first group of problems involved nonlinear systems which could be either solved exactly or reduced by some means to a linear system. These not only included exact methods but also, in some cases, approximate techniques where the stability of the linearized system yields useful properties about the stability of equilibrium of the nonlinear system.
