ABSTRACT
This chapter considers the stability analysis of a system, the dynamics of which are represented in time domain by nonlinear time-invariant ordinary differential equations, is considered. It examines mathematical model for nonlinear systems and qualitative behavior of second-order linear time-invariant systems. The chapter discusses the Lipschitz conditions. Although in theory, the simulation could be proposed as a solution for the stability analysis, it is impractical or impossible, since in nonlinear system studies, every initial condition should be used. In a linear system with non-singular, the sole equilibrium state is the origin. In the nonlinear case, the equilibrium state could be an isolated one, similar to a linear system, or infinitely many isolated equilibrium states, or there could be a continuum of equilibrium states.
