Hurwitz matrix
E714449
The Hurwitz matrix is a structured matrix constructed from the coefficients of a polynomial and used to determine system stability in control theory via the Routh–Hurwitz criterion.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concept in control theory
ⓘ
concept in linear systems theory ⓘ matrix ⓘ structured matrix ⓘ |
| appearsIn |
classical control theory textbooks
ⓘ
courses on linear systems and control ⓘ |
| appliesTo |
characteristic polynomials of dynamical systems
ⓘ
real-coefficient polynomials ⓘ |
| associatedWith |
linear time-invariant differential equations
ⓘ
transfer functions in control systems ⓘ |
| basedOn | coefficients of a polynomial ⓘ |
| constructedFrom |
even-indexed coefficients of a polynomial
ⓘ
odd-indexed coefficients of a polynomial ⓘ ordered coefficients of a polynomial ⓘ |
| criterionFor | all roots of a polynomial having negative real parts ⓘ |
| describesProperty | Hurwitz stability of a polynomial ⓘ |
| field |
applied mathematics
ⓘ
control engineering ⓘ systems and control ⓘ |
| generalizationOf | Hurwitz determinants for higher-degree polynomials NERFINISHED ⓘ |
| hasAlternativeName | Hurwitz stability matrix NERFINISHED ⓘ |
| hasProperty |
entries are polynomial coefficients or zeros
ⓘ
principal minors encode stability information ⓘ size depends on the degree of the polynomial ⓘ |
| hasPurpose |
to determine stability of a linear system
ⓘ
to test whether all roots of a polynomial lie in the open left half-plane ⓘ |
| matrixType |
Toeplitz-like matrix
ⓘ
square matrix ⓘ |
| namedAfter | Adolf Hurwitz NERFINISHED ⓘ |
| relatedConcept |
Jury stability criterion
NERFINISHED
ⓘ
Nyquist stability criterion NERFINISHED ⓘ Routh–Hurwitz theorem NERFINISHED ⓘ root locus method ⓘ |
| relatedTo |
Hurwitz determinant
ⓘ
Hurwitz stability criterion NERFINISHED ⓘ Lyapunov stability NERFINISHED ⓘ Routh array NERFINISHED ⓘ characteristic equation of a linear system ⓘ |
| usedBy |
applied mathematicians
ⓘ
control engineers ⓘ systems theorists ⓘ |
| usedFor |
algebraic stability tests without computing roots
ⓘ
checking necessary and sufficient conditions for stability ⓘ computing Hurwitz determinants ⓘ |
| usedIn |
Routh–Hurwitz stability criterion
NERFINISHED
ⓘ
control theory ⓘ polynomial stability tests ⓘ stability analysis of linear time-invariant systems ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.