Name
Title | ||
|---|---|---|
Invariance properties in the root sensitivity of time-delay systems with double imaginary roots |
Abstract | ||
|---|---|---|
If iω∈iR is an eigenvalue of a time-delay system for the delay τ0 then iω is also an eigenvalue for the delays τk≔τ0+k2π/ω, for any k∈Z. We investigate the sensitivity, periodicity and invariance properties of the root iω for the case that iω is a double eigenvalue for some τk. It turns out that under natural conditions (the condition that the root exhibits the completely regular splitting property if the delay is perturbed), the presence of a double imaginary root iω for some delay τ0 implies that iω is a simple root for the other delays τk, k≠0. Moreover, we show how to characterize the root locus around iω. The entire local root locus picture can be completely determined from the square root splitting of the double root. We separate the general picture into two cases depending on the sign of a single scalar constant; the imaginary part of the first coefficient in the square root expansion of the double eigenvalue. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.automatica.2010.03.014 | Automatica |
Keywords | Field | DocType |
Time-delay systems,Sensitivity,Perturbation analysis,Imaginary axis,Root locus,Double roots,Critical delays | Perturbation theory,Functional square root,Control theory,Mathematical analysis,Scalar (physics),Square root of 3,Complex plane,Root locus,Square root,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
46 | 6 | 0005-1098 |
Citations | PageRank | References |
11 | 0.92 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jarlebring Elias | 1 | 84 | 11.48 |
| Wim Michiels | 2 | 513 | 77.24 |