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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.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 wikiPageID "1705432".
- Routh–Hurwitz_stability_criterion wikiPageRevisionID "600059250".
- 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 "Criterio di Routh".
- Routh–Hurwitz_stability_criterion label "Kryterium stabilności Hurwitza".
- Routh–Hurwitz_stability_criterion label "Routh–Hurwitz stability criterion".
- Routh–Hurwitz_stability_criterion label "Критерий устойчивости Гурвица".
- Routh–Hurwitz_stability_criterion label "معيار راوث-هورتز للاستقرارية".
- Routh–Hurwitz_stability_criterion label "ラウス・フルビッツの安定判別法".
- Routh–Hurwitz_stability_criterion sameAs Routh%E2%80%93Hurwitz_stability_criterion.
- 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 Q2621270.
- Routh–Hurwitz_stability_criterion sameAs Q2621270.
- Routh–Hurwitz_stability_criterion wasDerivedFrom Routh–Hurwitz_stability_criterion?oldid=600059250.