H∞ control for nonlinear systems with interval non-differentiable time-varying delay

In this paper, we develop a linear matrix inequality approach for studying H∞H∞ control problem for a class of nonlinear systems with interval time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. The key features approach includes the construction of new Lyapunov–Krasovskii functionals and the use of a tighter bounding technique. Improved delay-dependent sufficient conditions for the H∞H∞ control with exponential stability of the system are established in terms of linear matrix inequalities (LMIs). An application to H∞H∞ control of uncertain linear systems with interval time-varying delay is also given. Numerical examples are given to show the effectiveness of the obtained results.