Abstract

The paper considers robust H_∞ control problem for a class of nonlinear systems with input and state delays and nonlinear perturbation. Based on matrix analysis theory and robust stability theory, a condition which rely on delay of robust asymptotic stability for the system is derived. And in this process, the proper integral form of Lyapunov function was chosen, the properties of the linear matrix inequality (LMI) and Schur lemma was used. Moreover, a corresponding state feedback H_∞ control law for the system was given to ensure the robust asymptotic stability of such systems. Finally, the feasibility and efficiency of the sufficient condition and control law were verified by numerical simulation and compare, which was conducted through the MATLAB.

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