ABSTRACT
This chapter shows some examples of stability analysis of physical systems. Proving stability with A. M. Lyapunov functions is very general: it even works for nonlinear and time-varying systems. The Lyapunov function can be interpreted as the generalization of the energy function in electrical systems. After World War II, systems and control theory flourished. The transfer function representation was the most popular representation for systems. The chapter discusses the external stability of systems; this is usually called the bounded-input, bounded-output (BIBO) stability. A system is BIBO stable if for zero initial conditions any bounded input always evokes a bounded output Bifurcation. If a sudden change of a model parameter value results in a change of the asymptotic behavior of the system. This model parameter is called the bifurcation parameter, and its specific value where the change occurs, is called the critical value. External Stability concepts related to the input–ouput behavior of the system.
