A scalable approach to compute delay margin of a class of neutral-type time delay systems. (English) Zbl 1467.34062
Consider linear delay equation of neutral type under the form
\[
\dot{x}(t)-E\dot{x}(t-\tau)=Ax(t)+Bx(t-\tau)
\]
where \(A,B,E\) are real constant \(n\times n\) matrices. The related characteristic equation is
\[
\det\Delta(s,e^{-s\tau})=\det(s(I_n-Ee^{-s\tau})-(A+Be^{-s\tau}))=0 .
\]
Assume that the spectral radius \(\rho(E)<1\) and that the equation is asymptotically stable for \(\tau=0\). The delay margin is defined as
\[
\tau^*=\min\{\tau>0: s=i\omega\text{ is a characteristic root for some } \omega\in\mathbb{R}^+\} .
\]
Necessary and sufficient conditions for the existence of \(\tau^*>0\) are established.
A scalable implementation of a numerical alrgorithm for finding \(\tau^*\) is provided.
Numerical examples are given.
A scalable implementation of a numerical alrgorithm for finding \(\tau^*\) is provided.
Numerical examples are given.
Reviewer: Nikita V. Artamonov (Moskva)
MSC:
| 34K06 | Linear functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 93D20 | Asymptotic stability in control theory |
| 65L03 | Numerical methods for functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 34K08 | Spectral theory of functional-differential operators |
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