Controller approximation: approaches for preserving H∞ performance

Investigates the design of reduced-order controllers using an H _∞ framework. Given a stabilizing controller which satisfies a prespecified level of closed-loop H_∞ performance, sufficient conditions are derived for another controller to be stabilizing and satisfy the same level of H_∞, performance. Such controllers are said to be (P,γ)-admissible, where P is the model of the plant under consideration and γ is the required level of prespecified H_∞ 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,γ)-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