A delta operator approach to discrete-time H ∞ control

To increase the performance of digitally implemented control laws, it is desirable to directly synthesize the digital control law. Hence, this paper considers the direct synthesis of discrete-time, H ∞ control laws. Previously, two approaches have been proposed to this problem. The most common method uses the bilinear transformation to convert the discrete-time problem into an equivalent continuous-time problem, allowing the controller to be synthesized with software developed for continuous-time systems. This method is often effective but requires unnecessary steps and is not applicable in all circumstances. The second approach is to synthesize the discrete-time, H ∞ control law by solving discrete-time, H ∞ Riccati equations. Due to numerical ill-conditioning, this approach can fail at sufficiently high sample rates. This numerical ill-conditioning can be eliminated by representing the discrete-time system and H ∞ controller using the delta operator. Hence, the H ∞ design equations for direct synthesis ...