State-space solution to a minimum-entropy $\mathcal{H}_\infty$-optimal control problem with a nested information constraint

Abstract

State-space formulas are derived for the minimum-entropy $\mathcal{H}_\infty$ controller when the plant and controller are constrained to be block-lower-triangular. Such a controller exists if and only if: the corresponding unstructured problem has a solution, a certain pair of coupled algebraic Riccati equations admits a mutually stabilizing fixed point, and a pair of spectral radius conditions is met. The controller's observer-based structure is also discussed, and a simple numerical approach for solving the coupled Riccati equations is presented.