Controller approximation: approaches for preserving H/sub /spl infin// performance

Investigates the design of reduced-order controllers using an H/sub /spl infin// framework. Given a stabilizing controller which satisfies a prespecified level of closed-loop H/sub /spl infin// performance, sufficient conditions are derived for another controller to be stabilizing and satisfy the same level of H/sub /spl infin//, performance. Such controllers are said to be (P,/spl gamma/)-admissible, where P is the model of the plant under consideration and /spl gamma/ is the required level of prespecified H/sub /spl infin// performance. The conditions are expressed as norm bounds on particular frequency-weighted errors, where the weights are selected to make a specific transfer function a contraction. The design of reduced-order (P,/spl gamma/)-admissible controllers is then formulated as a frequency-weighted model reduction problem. It is advantageous for the required weights to be large in some sense. Solutions which minimize either the trace, or the determinant, of the inverse weights are characterized. We show that the procedure for minimizing the determinant of the inverse weights always gives a direction where the weights are the best possible. To conclude, we demonstrate by way of a numerical example, that when used in conjunction with a combined model reduction/convex optimization scheme, the proposed design procedures are effective in substantially reducing controller complexity.