H∞ control for delay systems: characterization with finite-dimensional operations

An H^∞ problem is discussed for a system with delays in control. By employing completing the square argument of particular quadratic forms, it is clarified that the solvability and the solution are characterized with finite-dimensional operations. The check method of solvability requires the stabilizing solutions to matrix Riccati equations with the maximal solution to a transcendental equation. The H^∞ control law is constructively given based on the solutions to matrix Riccati equations. A game theoretic interpretation is provided on the trade-off between the initial uncertainties and attenuating the disturbances