This paper presents a new method for the design of control laws for systems with on-off nonlinear actuators. The new methodology improves the design of control laws for pulse-modulated systems by allowing the use of continuous-time multi-inputlmultioutput design procedures. Discrete-time state feedback control gains are developed from the "digital redesign" of continuous-time feedback gains, based on a geometric series approximation, to closely match the states of the closed-loop hybrid system to those of the original designed closed-loop continuous-time system at each sampling instant. A delay is then incorporated into a pulse-width modulator design to closely match the states of the modulated system to those of the discrete-time pulse-amplitude modulated system. The delay time is improved from previous work to provide a close match between the states for pulse durations of all sizes, in effect matching the states of the pulse-width modulated system to those of the closed-loop continuous-time system. The new control law design is applied to the problem of attitude control of the Space Shuttle Orbiter with the Hubble Space Telescope deployed on its remote manipulator. * Senior Member Technical Staff. Member A I M . t Professor, Electrical Engineering. Member AIAA. tt Aerospace Engineer. Member AIAA. Copyright O 1995 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Many paradigms are available for the synthesis of control laws for continuous-time systems, and though many methods also exist for developing discrete-time or digital controllers, it is often desirable to design a control law for the continuous-time plant. It is often more direct to determine the control specifications in the continuous-time or frequency domain. Also, direct digital control law design has difficulty in predetermining the hybrid control specifications and ignores inter sampling effects. Yet, these continuoustime control laws are generally implemented via discrete-time computer control, requiring that a discrete-time control, equivalent to the continuous-time control, be developed. The process of developing discrete-time control laws that provide closed-loop performance of the hybrid system equivalent to the performance of the designed closed-loop continuoustime system is known as "digital redesign". Several techniques have been developed to digitally redesign continuous-time feedback controllers[l] ,[2] ,[3]. Unfortunately, the principal applied for the design of discrete-time control laws, i.e., that the amplitude of the control signal can take any finite value, which is why discrete-time control is often referred to as pulse-amplitude control (PAM), is not valid for all computer controlled systems. Systems that utilize onoff control devices, such as the reaction jet or electronic relay, can only provide a single finite value of control. To provide control with these types of actuator, either complex non-linear algorithms[4] must be developed or the control must be applied by modulating the pulse width, the pulse frequency or both the pulse width and frequency. These modulation techniques, in particular pulse-width modulation (PWM), allow the design of linear control laws to control non-linear systems. Although methods exist for the design of linear control laws for pulse width modulation systems[5], they still