Direct H∞ Design Methods for Finite Precision Controller Synthesis and Realization

The finite precision nature of digital hardware makes it necessary to consider the effects of finite wordlength (FWL) when performing a controller design. Most studies on these issues only consider the optimal FWL implementation for a given controller without regard to the controller synthesis. It is known that such "optimal realization" is not optimal overall. In this paper, the direct methods for FWL controller synthesis and realization are addressed. The effects of finite wordlength are taken into account when the controller is synthesized thus the closed loop with FWL controller also meets some desired performance objectives. An FWL H_infin controller design problem is presented. A numerical example is included to verify the theoretical analysis and to illustrate the proposed design procedure