Necessary stability conditions for neutral-type systems with multiple commensurate delays

ABSTRACT

Necessary stability conditions depending on the Lyapunov matrix for neutral-type systems with commensurate delays are presented. In order to obtain them, further results are introduced: the computation of the Lyapunov–Krasovskii functional of complete-type by a new Cauchy formula and the introduction of identities that relate the fundamental and the Lyapunov matrix of the system. The main result is illustrated by some examples.

KEYWORDS:

• Neutral-type systems with multiple delays
• necessary stability conditions
• Lyapunov–Krasovskii functionals
• delay Lyapunov matrix

Acknowledgments

We thank the anonymous reviewers for their insightful comments that helped improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Russian Foundation for Basic Research (RFBR) [grant number 16-31-00436 a]. Consejo Nacional de Ciencia y Tecnología [grant number 180725].