Explicit formulas for operator Riccati equations arising in H∞ control with delays

Standard H^∞-control problems are discussed for a system with delays in control. For the operator Riccati equations arising in full-information control problem, a necessary and sufficient condition on the solvability is clarified in the framework of finite-dimensional operations. The check method of solvability requires a stabilizing solution to matrix Riccati equation with a maximal solution to a transcendental equation. The analytic solution is constructively given based on the matrix Riccati equation. By employing the results derived here, the design procedure of H^∞ output feedback law is illustrated with finite-dimensional operations. The operator Riccati equation plays an essential part of H^∞ control/estimation problems and enables us to characterize the optimal strategy which depends on delayed informations or actions