Finite-gain [Formula: see text] stability from disturbance to output of a class of time delay system.

Results on finite-gain \(\mathcal{L_{\infty}}\) stability from a disturbance to the output of a time-variant delay system are presented via a delay decomposition approach. By constructing an appropriate Lyapunov-Krasovskii functional and a novel integral inequality, which gives a tighter upper bound than Jensen’s inequality and Bessel-Legendre inequality, some sufficient conditions are established and desired feedback controllers are designed in terms of the solution to certain LMIs. Compared with the existing results, the obtained criteria are more effective due to the tuning scalars and free-weighting matrices. Numerical examples and their simulations are given to demonstrate the effectiveness of the proposed method.