Stable polynomial

A polynomial is defined to be stable in two different ways.

• Hurwitz-stable: In the context of a differential equation (continuous-time) the characteristic polynomial is stable if all its roots lie in the open left complex half-plane.
• Schur-stable: In the context of a difference equation (discrete-time), its characteristic polynomial is stable if all its roots lie in the opencomplex unit disk.

Also, in control theory, a linear, time-invariant system (see LTI system theory) is said to be BIBO stable if every bounded input produces bounded output. A linear system is BIBO stable if its denominator characteristic polynomial is stable (Hurwitz stable for a continuous-time system, Schur stable for discrete-time). In practice, stability is tested via several stability criteria.