Stability results for point time-delay systems obtained via rouche's theorem

Abstract

This article deals with asymptotic stability and stabilization criteria based on Rouche's theorem for variation of zeros of analytic functions within complex domains. Stability criteria consisting of sufficiency conditions for asymptotic stability of time-invariant point delay systems are obtained, provided that an auxiliary delay-free system is globally asymptotically stable, in terms of smallness of the delayed dynamics related to such a free-delay dynamics. A physical insight related to the use of the stability criteria linked with the variations of the auxiliary system are also given. Finally, some extensions related to closed-loop stabilization using such stability criteria are also given.

Keywords:

• Delay systems
• Asymptotic stability
• Rouche's theorem
• AMS Subject Classification: 93D20
• 34D23
• 30D20
• 30D30

Acknowledgments

The authors are very grateful to DGES and UPV/EHU for their partial support of this work through projects DPI 2000-0244 and 1/UPV/EHU 00I06.I06- EB 8235/2000, respectively.

Notes

^†E-mails: [email protected]

Additional information

Notes on contributors

R. Barcena †

†E-mails: [email protected]