Robust stability under structured and unstructured perturbations
- 1 January 1990
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 35 (10) , 1100-1108
- https://doi.org/10.1109/9.58552
Abstract
The problem of robust stability for linear time-invariant single-output control systems subject to both structured (parametric) and unstructured (H/sub infinity /) perturbations is studied. A generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time-invariant dynamic system under perturbations of mixed type is presented. The solution involves calculating the H/sub infinity /-norm of a finite number of extremal plants. The problem of calculating the exact structured and unstructured stability margins is then constructively solved. A feedback control system containing a linear time-invariant plant which is subject to both structured and unstructured perturbations is considered. The case where the system to be controlled is interval is treated, and a nonconservative, easily verifiable necessary and sufficient condition for robust stability is given. The solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered.Keywords
This publication has 7 references indexed in Scilit:
- Stability margins for Hurwitz polynomialsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Robustness in the presence of mixed parametric uncertainty and unmodeled dynamicsIEEE Transactions on Automatic Control, 1991
- Robust stability of feedback control systems with uncertain parameters and unmodeled dynamicsMathematics of Control, Signals, and Systems, 1990
- A generalization of Kharitonov's theorem; Robust stability of interval plantsIEEE Transactions on Automatic Control, 1989
- A necessary and sufficient condition for robust BIBO stabilitySystems & Control Letters, 1988
- A Course in H∞ Control TheoryPublished by Springer Nature ,1987
- Feedback Systems: Input-Output PropertiesJournal of Dynamic Systems, Measurement, and Control, 1975