The robustness of feedback systems with bounded complexity controllers
- 1 June 1996
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 41 (6) , 795-803
- https://doi.org/10.1109/9.506232
Abstract
H/sub /spl infin// methods for the analysis and design of robust feedback control systems have sometimes been criticized for an apparent conservatism. However, recent results have shown that they can provide the least conservative results possible under a particular set of assumptions. For example, a ball in the v-gap metric is the largest set of plants that can be guaranteed to be stabilized a priori by a controller known only to satisfy a bound on the induced norm of a particular closed-loop operator. Nevertheless, there are examples of uncertainty which, whilst large when measured by the v-gap metric, would be regarded as relatively benign by an experienced designer of control systems. The present paper examines the possibility that in arriving at this judgment, such a designer is implicitly using the knowledge that he will always choose the least complex controller necessary to do the job. It is shown that, given an appropriate bound on the complexity of the controller, significantly stronger a priori robustness results can be obtained.Keywords
This publication has 11 references indexed in Scilit:
- Conservatism of the gap metricIEEE Transactions on Automatic Control, 1993
- Frequency domain uncertainty and the graph topologyIEEE Transactions on Automatic Control, 1993
- A loop-shaping design procedure using H/sub infinity / synthesisIEEE Transactions on Automatic Control, 1992
- The stability robustness of generalized eigenvaluesIEEE Transactions on Automatic Control, 1992
- Robust Design in the Graph Topology; A Benchmark ExamplePublished by Institute of Electrical and Electronics Engineers (IEEE) ,1992
- Feedback stability under simultaneous gap metric uncertainties in plant and controllerSystems & Control Letters, 1992
- A four-block problem for H∞ design: Properties and applicationsAutomatica, 1991
- Optimal robustness in the gap metricIEEE Transactions on Automatic Control, 1990
- State-space solutions to standard H/sub 2/ and H/sub infinity / control problemsIEEE Transactions on Automatic Control, 1989
- On the metric complexity of casual linear systems: ε -Entropy and ε -Dimension for continuous timeIEEE Transactions on Automatic Control, 1979