Abstract
The principal results of the qualitative approach include the stability properties of an equilibrium point (rest position) and the boundedness of solutions of ordinary differential equations. This chapter presents the concept of an equilibrium point and defines the various types of stability, instability, and boundedness concepts. It discusses the stability properties of autonomous and periodic systems and the stability properties of linear systems. The main stability results from the existence of certain real valued functions called Lyapunov functions. The main stability, instability, and boundedness results constitute the direct method of Lyapunov (of stability analysis). The chapter discusses the linear systems in the context of the Lyapunov theory. The stability results constitute sufficient conditions for the extensions and improvements of the Lyapunov theory.
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