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- Routh–Hurwitz_stability_criterion abstract "In control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time invariant (LTI) control system. The Routh test is an efficient recursive algorithm that English mathematician Edward John Routh proposed in 1876 to determine whether all the roots of the characteristic polynomial of a linear system have negative real parts. German mathematician Adolf Hurwitz independently proposed in 1895 to arrange the coefficients of the polynomial into a square matrix, called the Hurwitz matrix, and showed that the polynomial is stable if and only if the sequence of determinants of its principal submatrices are all positive. The two procedures are equivalent, with the Routh test providing a more efficient way to compute the Hurwitz determinants than computing them directly. A polynomial satisfying the Routh–Hurwitz criterion is called a Hurwitz polynomial.The importance of the criterion is that the roots p of the characteristic equation of a linear system with negative real parts represent solutions ept of the system that are stable (bounded). Thus the criterion provides a way to determine if the equations of motion of a linear system have only stable solutions, without solving the system directly. For discrete systems, the corresponding stability test can be handled by the Schur–Cohn criterion, the Jury test and the Bistritz test. With the advent of computers, the criterion has become less widely used, as an alternative is to solve the polynomial numerically, obtaining approximations to the roots directly.The Routh test can be derived through the use of the Euclidean algorithm and Sturm's theorem in evaluating Cauchy indices. Hurwitz derived his conditions differently.".
- Routh–Hurwitz_stability_criterion wikiPageExternalLink Routh-HurwitzTheorem.html.
- Routh–Hurwitz_stability_criterion wikiPageExternalLink 1.
- Routh–Hurwitz_stability_criterion wikiPageExternalLink 25956-routh-hurwitz-stability-test.
- Routh–Hurwitz_stability_criterion wikiPageID "1705432".
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- Routh–Hurwitz_stability_criterion wikiPageRevisionID "673544351".
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Adolf_Hurwitz.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink American_Journal_of_Physics.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink BIBO_stability.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Bistritz_stability_criterion.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Category:Electronic_amplifiers.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Category:Electronic_feedback.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Category:Polynomials.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Category:Signal_processing.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Category:Stability_theory.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Cauchy_index.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Characteristic_polynomial.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Control_engineering.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Control_system.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Control_theory.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Derivation_of_the_Routh_array.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Edward_John_Routh.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Edward_Routh.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Equations_of_motion.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Euclidean_algorithm.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Euclids_algorithm.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Felix_Gantmacher.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Fundamental_theorem_of_algebra.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Hurwitz_polynomial.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Jury_stability_criterion.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Kharitonovs_theorem.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Linear_function.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Linear_system.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Liénard–Chipart_criterion.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Minor_(linear_algebra).
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Nyquist_stability_criterion.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Oxford_University_Press.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Richard_C._Dorf,_Robert_H._Bishop.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Root_locus.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Root_of_a_function.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Routh-Hurwitz_stability_criterion.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Routh–Hurwitz_stability_criterion.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Routh–Hurwitz_theorem.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Stable_polynomial.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Sturms_theorem.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Sylvester_matrix.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Time-invariant_system.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Time_invariant.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Transfer_function.
- Routh–Hurwitz_stability_criterion wikiPageWikiLink Zero_of_a_function.
- Routh–Hurwitz_stability_criterion wikiPageWikiLinkText "Routh".
- Routh–Hurwitz_stability_criterion wikiPageWikiLinkText "Routh–Hurwitz criterion".
- Routh–Hurwitz_stability_criterion wikiPageWikiLinkText "Routh-Hurwitz".
- Routh–Hurwitz_stability_criterion wikiPageWikiLinkText "Routh–Hurwitz criterion".
- Routh–Hurwitz_stability_criterion wikiPageWikiLinkText "Routh–Hurwitz stability criterion".
- Routh–Hurwitz_stability_criterion wikiPageWikiLinkText "Routh–Hurwitz".
- Routh–Hurwitz_stability_criterion hasPhotoCollection Routh–Hurwitz_stability_criterion.
- Routh–Hurwitz_stability_criterion wikiPageUsesTemplate Template:Cite_book.
- Routh–Hurwitz_stability_criterion wikiPageUsesTemplate Template:Cite_journal.
- Routh–Hurwitz_stability_criterion wikiPageUsesTemplate Template:Refimprove.
- Routh–Hurwitz_stability_criterion wikiPageUsesTemplate Template:Reflist.
- Routh–Hurwitz_stability_criterion subject Category:Electronic_amplifiers.
- Routh–Hurwitz_stability_criterion subject Category:Electronic_feedback.
- Routh–Hurwitz_stability_criterion subject Category:Polynomials.
- Routh–Hurwitz_stability_criterion subject Category:Signal_processing.
- Routh–Hurwitz_stability_criterion subject Category:Stability_theory.
- Routh–Hurwitz_stability_criterion comment "In control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time invariant (LTI) control system. The Routh test is an efficient recursive algorithm that English mathematician Edward John Routh proposed in 1876 to determine whether all the roots of the characteristic polynomial of a linear system have negative real parts.".
- Routh–Hurwitz_stability_criterion label "Routh–Hurwitz stability criterion".
- Routh–Hurwitz_stability_criterion sameAs معيار_راوث-هورتز_للاستقرارية.
- Routh–Hurwitz_stability_criterion sameAs Criterio_di_Routh.
- Routh–Hurwitz_stability_criterion sameAs ラウス・フルビッツの安定判別法.
- Routh–Hurwitz_stability_criterion sameAs Kryterium_stabilności_Hurwitza.
- Routh–Hurwitz_stability_criterion sameAs m.05pwvs.
- Routh–Hurwitz_stability_criterion sameAs Критерий_устойчивости_Гурвица.
- Routh–Hurwitz_stability_criterion sameAs Kriteri_i_Routh-it.
- Routh–Hurwitz_stability_criterion sameAs Критерій_стійкості_Гурвіца.
- Routh–Hurwitz_stability_criterion sameAs Q2621270.
- Routh–Hurwitz_stability_criterion sameAs Q2621270.
- Routh–Hurwitz_stability_criterion wasDerivedFrom Routh–Hurwitz_stability_criterion?oldid=673544351.
- Routh–Hurwitz_stability_criterion isPrimaryTopicOf Routh–Hurwitz_stability_criterion.