In the context of the characteristic polynomial of a differential equation or difference equation, a polynomial is said to be stable if either: The first condition provides stability for continuous-time linear systems, and the second case relates to stability of discrete-time linear systems.
Stable polynomials arise in control theory and in mathematical theory of differential and difference equations.
A linear, time-invariant system (see LTI system theory) is said to be BIBO stable if every bounded input produces bounded output.
Just as stable polynomials are crucial for assessing the stability of systems described by polynomials, stability matrices play a vital role in evaluating the stability of systems represented by matrices.
A matrix A is a Schur (stable) matrix if its eigenvalues are located in the open unit disk in the complex plane.