This study deals with the problem of exponential stability analysis for a class of singular systems with interval time-varying discrete and distributed delays. By constructing a set of improved Lyapunov–Krasovskii functionals, new delay-dependent conditions are established in terms of linear matrix inequalities ensuring the regularity, impulse free and exponential stability of the system. This approach allows the authors to compute simultaneously the two bounds that characterise the exponential stability rate of the solution by various efficient convex optimisation algorithms. Numerical examples are given to illustrate the effectiveness of the obtained results.