On the Lyapunov matrices for integral delay systems

ABSTRACT

We study Lyapunov matrices for the class of integral delay systems with constant kernel and one delay. The uniqueness and computational issues of these Lyapunov matrices for exponentially stable systems are investigated.

Keywords:

• Integral delay systems
• Lyapunov–Krasovskii functionals
• Lyapunov matrices

Acknowledgments

The authors thank to the anonymous reviewers for their useful comments and suggestions that help us to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

H. Arismendi-Valle  http://orcid.org/0000-0002-9165-4354

D. Melchor-Aguilar http://orcid.org/0000-0002-4751-9147

Additional information

Funding

H. Arismendi-Valle thanks to Consejo Nacional de Ciencia y Tecnología (CONACYT) for the Ph.D. scholarship.

Notes on contributors

H. Arismendi-Valle

H. Arismendi-Valle was born in Mexico city in the year 1989. He received the MSc degree in automatic control at the Department of Automatic Control in CINVESTAV-IPN, México in 2014 and the Ph.D. degree in Control and dynamic systems at the Division of Applied Mathematics in IPICYT, México in 2019. His research interests are, and not limited to, functional equations with delay, Lyapunov matrices and integral delay systems.

D. Melchor-Aguilar

D. Melchor-Aguilar was born in 1974. He received the MSc degree in electric engineering and the PhD degree in automatic control from CINVESTAV-IPN, México in 1999 and 2002, respectively. From September 2002 to August 2003, he was a postdoctoral research fellow at HEUDIASYC-CNRS, Université de Technologie de Compiégne, France. In 2003, he joined the Division of Applied Mathematics at IPICYT, México where he is currently a professor. Currently, he is an associate editor of European Journal of Control. He received the PhD thesis Award from CINVESTAV-IPN, México in 2003. His research interests are functional equations with delay, stability and robust stability theory.