Approximation of delay Lyapunov matrices

ABSTRACT

The paper deals with the computation of delay Lyapunov matrices for linear exponentially stable time-invariant systems with several pointwise delays. It is shown that the matrices depend continuously on the system delays. Based on this theoretical result, an algorithm of approximation of the delay Lyapunov matrices with a prescribed accuracy is presented. The result is illustrated by an example.

KEYWORDS:

• Time-delay system
• Lyapunov matrix
• Lyapunov–Krasovskii approach
• complete-type functional
• approximation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Russian Foundation for Basic Research [grant number 16-31-00436].