Stability and Instability of Linear Systems with Discrete Spectra

Abstract

The terms stability and instability are now so widely used that unless there are additional explanations it is almost always impossible to understand what is being discussed. The subject may be the stability of the system as a whole, the stability of its completely defined motion (trajectory or solution), or the stability of the equilibrium, etc. There are even different types of stability and instability. There may be stability in the large, which means with respect to arbitrary disturbances, or stability in the small, which is defined by the properties of the linearized equations. The qualifier to the word instability usually characterizes the physical mechanism by which the oscillation arises rather than the mathematical properties, i.e., dissipative instability, parametric instability, radiational instability etc.