On exponential stability of continuous-time linear systems with distributed state delay: An asymmetric functional approach

This paper focuses on the problem of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> -exponential stability of continuous-time linear systems with both discrete and distributed time-varying delays (DT-VDs). Tractable conditions ensuring exponential convergence with prescribed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> -decaying rate are derived using a novel asymmetric Lyapunov–Krasovskii functional (A-LKF) approach. Numerical examples with simulations are presented to demonstrate the effectiveness of the obtained results.