Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays

This paper is concerned with the robust H∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H∞ disturbance rejection attenuation level. By introducing a new Lyapunov-Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton-Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.