H infinity Control for Non-Linear Systems with Dependent Time-Delay in State and Input

The design of robust H_∞ controller for a class of uncertain non-linear systems with time-varying state delay and input control delay is considered. The uncertainties are norm-bounded and the states of the uncertain systems are available. A new sufficient condition of robust stability control law is given for the non-linear systems by constructing Lyapunov function, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. The state feedback H_∞ control law can be obtained by solving the corresponding linear matrix inequality. At last, a numerical example is presented to illustrate the validity and feasibility of this approach.