×

Some new results on the asymptotic stability of uncertain dynamical systems with time-varying delay. (English) Zbl 1049.93071

The author studies the stability in the first approximation of \[ \dot{x}=Ax(t) + f(x_t,t) \] with \(A\) a Hurwitz matrix and \(f:C(-h,0; \mathbb{R}^n)\rightarrow \mathbb{R}^n\) a sublinear functional satisfying \(\| f(\psi,t)\| <\alpha\| \psi\| \), using a quadratic Razumikhin-like function \(V(x) = x^{T}Px\) with \(P\) solution to the Lyapunov equation \[ A^{T}P+PA+Q=0\;,\;Q>0. \] Some academic applications to robustness are given.

MSC:

93D20 Asymptotic stability in control theory
93C23 Control/observation systems governed by functional-differential equations
34K20 Stability theory of functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1109/9.256406 · Zbl 0770.93077 · doi:10.1109/9.256406
[2] DOI: 10.1007/BF02192220 · Zbl 0816.93074 · doi:10.1007/BF02192220
[3] Wu H. S., ControlTheory and Advanced Technology 10 pp 1147– (1995)
[4] DOI: 10.1016/0167-6911(94)90071-X · Zbl 0805.93045 · doi:10.1016/0167-6911(94)90071-X
[5] DOI: 10.1109/9.668851 · Zbl 0912.93053 · doi:10.1109/9.668851
[6] HALE J., Theory of Functional Differential Equations (1977) · Zbl 0352.34001
[7] DOI: 10.1080/00207729708929486 · Zbl 0899.93029 · doi:10.1080/00207729708929486
[8] CHEN, WANYI. 1998.On the robust stabilization of uncertain linear systems with time-delay. In Proceedings of the 1998 Chinese Control Conference, 101104Beijing: National Defence University Press. · Zbl 1052.93050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.