Sampled-data control of homogeneous system with uncertain time delay in the input

The paper investigates stabilization problem of a class of systems (homogeneous systems) with a large uncertain time delay in the input. By the homogeneous property, this problem is first transformed to stabilize the same system with a small time delay in the input. To solve the resulted problem, we first present a sampled-data controller which is easy to design to stabilize the Euler approximate discrete-time model of the homogeneous system without input delay. Then, we prove that this sampled-data controller also stabilizes the homogeneous system with a small time delay in the input if some conditions are satisfied. Based on these results, we give detailed analysis and design steps for the stabilization problem of the original problem.