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 stability
of 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 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. 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.
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...
strictly negative, excluding the imaginary axis (i.e., a Hurwitz stablepolynomial). A polynomial function P(s) of a complex variable s is said to be Hurwitz...
Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves. A numerically stable way to evaluate polynomials in...
Positive systems Radial basis function Root locus Signal-flow graphs Stablepolynomial State space representation Steady state Transient response Transient...
be replaced with inequalities between Hilbert polynomials. Narasimhan–Seshadri theorem says that stable bundles on a projective nonsingular curve are...
invariant (LTI) system is stable proposed by Yuval Bistritz. Stability of a discrete LTI system requires that its characteristic polynomial D n ( z ) = d 0 +...
Process control Robust decision making Root locus Servomechanism Stablepolynomial State space (controls) System identification Stability radius Iso-damping...
the polynomial p {\displaystyle p} . It was established by Adolf Hurwitz in 1895 that a real polynomial with a 0 > 0 {\displaystyle a_{0}>0} is stable (that...
polynomials has transcendence degree dim(V) – dim(G). A point of the corresponding projective space of V is called unstable, semi-stable, or stable if...
In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes...
Polynomial matrices are widely studied in the fields of systems theory and control theory and have seen other uses relating to stablepolynomials. In...
Positive systems Radial basis function Root locus Signal-flow graphs Stablepolynomial State space representation Steady state Transient state Underactuation...
polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial....
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the...
abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous...
complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers. Quadratic polynomials have the following...
In algebra, an alternating polynomial is a polynomial f ( x 1 , … , x n ) {\displaystyle f(x_{1},\dots ,x_{n})} such that if one switches any two of the...
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number...
their response to disturbances. stablepolynomial That class of polynomials representing the transfer functions of stable control systems. stacking factor...
of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in...
thus, their stability function is a polynomial. It follows that explicit Runge–Kutta methods cannot be A-stable. The stability function of implicit Runge–Kutta...
adjacent stable matchings in the lattice. The family of all rotations and their partial order can be constructed in polynomial time, leading to polynomial time...
to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called...
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