Robust control in the gap: a state-space solution in the presenceof a single input delay

A solution is provided to the problem of (sub)optimal robust design in the gap for a system with a single input lag. The problem is shown to reduce to two matrix algebraic Riccati equations that solve an allied linear-quadratic-Gaussian/H₂ problem and a parameterized differential matrix Riccati equation. The analysis intertwines finite-dimensional delay equations and distributed abstract evolution models. The parameterized family of suboptimal compensators is presented in terms of a neutral equation model