Polynomials | Stability theory

Stable polynomial

In the context of the characteristic polynomial of a differential equation or difference equation, a polynomial is said to be stable if either: * all its roots lie in the open left half-plane, or * all its roots lie in the open unit disk. The first condition provides stability for continuous-time linear systems, and the second case relates to stabilityof discrete-time linear systems. A polynomial with the first property is called at times a Hurwitz polynomial and with the second property a Schur polynomial. Stable polynomials arise in control theory and in mathematical theoryof 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. A linear system is BIBO stable if its characteristic polynomial is stable. The denominator is required to be Hurwitz stable if the system is in continuous-time and Schur stable if it is in discrete-time. In practice, stability is determined by applying any one of several stability criteria. (Wikipedia).

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Related pages

Differential equation | Coefficient | Jury stability criterion | Stability radius | Root of unity | Polynomial | Unit disk | Hurwitz polynomial | Degree of a polynomial | BIBO stability | Stability criterion | Control theory | Routh–Hurwitz theorem | Routh–Hurwitz stability criterion | Real number | Time-invariant system | Liénard–Chipart criterion | Stability theory | Möbius transformation | Characteristic equation (calculus) | Bistritz stability criterion | Schur polynomial | Open set