Robust Schur Stability of a Polynomial Matrix Family

Kalinina, Elizaveta A.; Smol’kin, Yuri A.; Uteshev, Alexei Yu.

doi:10.1007/978-3-030-26831-2_18

Cited by 3 publications

(2 citation statements)

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“…Unfortunately, the computational difficulties grow tremendously with the increase in the number of variables and order of the manifolds (traditional curse of symbolic algorithms). For instance, in [26], the problem of robust Schur stability of the order 3 matrix family depending on 3 parameters leads to the distance equation of the order 162.…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, the distance from u 0 to the Hopf quadric equals √ z * ≈ 2.4898. To find the nearest point on the quadric, we first evaluate the multiple zero for the polynomial 1 (μ, z * ) (defined by (26)) via formula (21) to get μ * ≈ −0.1508. Then, we apply formula (24): Check u 0 − u * = √ z * , L 1 (u * ) = 0 and u 0 − u * is normal to the Hopf quadric at u = u * , i.e., it is parallel to the gradient to this quadric at u * :…”

Section: Examplesmentioning

confidence: 99%

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Measuring the criticality of a Hopf bifurcation

Uteshev

Kalmár‐Nagy

2020

Nonlinear Dyn

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This work is based on the observation that the first Poincaré–Lyapunov constant is a quadratic function of the coefficients of the two-dimensional vector field at a Hopf bifurcation. From a given parameter point, we find the distance to the “Hopf quadric.” This distance provides a measure of the criticality of the Hopf bifurcation. The viability of the approach is demonstrated through numerical examples.

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Section: Resultsmentioning

confidence: 99%