Novel delay-dependent stability criterion for time-varying delay systems with parameter uncertainties and nonlinear perturbations

• The stability analysis for uncertain delay systems with nonlinear perturbations.
• Partitioning the time-varying delay into non-uniformly subintervals.
• Decomposing the corresponding integral intervals based on time delay.
• Introducing γ   (0<γmin{1τd,1}) in the Lyapunov–Krasovskii functional.
• Some new variables are defined to deal with uncertain parameters.

This study proposes a novel approach to obtain less conservative conditions for the robust stability analysis for time-varying delay systems with parameter uncertainties and nonlinear perturbations. Specifically, first, we divide the time-varying delay into non-uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms more exactly. Second, novel delay-derivation-dependent stability criteria are derived by introducing a parameter γγ in the Lyapunov–Krasovskii functional. Third, we define some new variables to deal with uncertain parameters. Finally, two numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.