Robust Stabilization Problem for Time Delay Systems Based on Spectral Decomposition Approach

A robust stabilization problem is discussed for a system with delays in state and control. We derive a robust stabilizing control law against additive perturbations. And farther, motivated by the structure of predictive controllers, we provide some interpretations on the structure of the required control law. The key point in the derivation is to employ a spectral decomposition argument for time delay systems. This approach first enables us to completely characterize the solvability of the robust stabilization problem based on finite-dimensional Riccati equations.