A differential game, time-domain interpretation of the H(infinity) control design problem

H-infinity control design consists of selecting a controller to minimize the effects of "worst-possible" disturbances. State-space solutions have been developed; however, previous efforts to derive and describe such solutions have been convoluted and complex.; This work formulates the H-infinity problem as a finite-horizon linear-quadratic differential game between the controller and a bounded worst disturbance; this formulation is dubbed the Linear-Quadratic Worst disturbance (LQW) problem. Both continuous and discrete-time systems are considered under conditions of full-state feedback, open-loop control, and output feedback.; State-space solutions follow from consideration of first-order necessary conditions by means of the calculus of variations. A completion of squares technique reveals differential game saddle-point conditions and provides direct, compelling proof of an optimal minimax solution.; The LQW controller structure resembles that of the Linear-Quadratic Gaussian (LQG) controller. The future control problem requires the solution of a Riccati equation with a mixed-definite control penalty reflecting beneficial control and adverse disturbance. The dual past filtering problem yields a Kalman filter solution with mixed-definite sensor penalties corresponding to a sensor term plus a tracking error term resulting from the disruptive disturbance influence. The LQG separation structure gives way to an LQW "connection" structure reflecting coupling between the past and future problems, leading to a 'resent problem" of determining the worst possible current state. The saddle-point conditions require positive semi-definiteness of the past and future Riccati solutions and positive-definiteness of their combination in the present.; Previous work indicates a zero worst measurement disturbance. Saddle-point considerations indicate that the process and measurement disturbances actually feed back estimator error as well as system state, but that the error mode is never excited along an optimal trajectory. The weighting of measurement disturbances in the disturbance bound nevertheless determines the estimator gains.; Extensions of the finite-horizon game to steady-state are explored and response to worst initial conditions examined.; Examples developed include a missile pursuit-evasion problem, maneuver and steady-state regulation of a helicopter near hover, and landing flare of a 747.