An l(infinity) approach to the design of linear multivariable controllers for discrete-time systems with hard time-domain constraints is presented. The notion of polar of the set of the exogenous inputs is used to parameterize the set of closed-loop transfer functions that meet regulation constraints. The constraints may include magnitude and rate bounds on all relevant process variables, including the control inputs. Solutions for optimal l(infinity) design are found by solving a linear program for the impulse-response coefficients of the controller, or for the coefficients of an ARMA controller model Using these formulations, an analytical framework is provided for delineating the tradeoffs that govern design of linear control systems.