State observer and robust control for delay systems

The paper considers the existing problems of state observer and the observer-based robust control problems for delay systems. The Lyapunov function method is applied through the paper. For a linear delay system, the necessary and sufficient condition for the system exists linear state observer is presented, and the observer-based robust controller design method is given. For nonlinear uncertain delayed system, the sufficient conditions for the system with linear and nonlinear state observers is presented respectively. The uncertainty which satisfies the Lipschitz condition and the corresponding observer-based robust controller design method are obtained.