Internally Positive Representation to Stability of Delayed Timescale-Type Differential- Difference Equation

Abstract

This paper considers exponential stability for a class of timescale-type differential-difference equation with bounded time-varying delay. Based on time scale theory, internally positive representation technique, as well as the existing exponential results of positive differential-difference equation on time scale, criteria of exponential stability of the system under consideration are obtained and they are robust to time delay and time scale to some extent. The theoretical results are applied to study stability for a class of linear singular system, and they are validated via two numerical examples.

Keywords

• Internally positive representation
• differential-difference equation
• time scale
• bounded delay
• stability analysis