Feedback limitations in nonlinear systems: from Bode integrals to cheap control
- 1 April 1999
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 44 (4) , 829-833
- https://doi.org/10.1109/9.754828
Abstract
Feedback limitations of nonlinear systems are investigated using the cheap control approach. The main result is that in the limit, when the control effort is free, the smallest achievable L/sub 2/ norm of the output is equal to the least amount of control energy (L/sub 2/ norm) needed to stabilize the unstable zero dynamics. This nonlinear result is structurally similar to an earlier linear result by Qiu and Davison (1993), which, in turn, is connected with a Bode-type integral derived by Middleton (1991).Keywords
This publication has 11 references indexed in Scilit:
- Trade-offs in linear control system designPublished by Elsevier ,2003
- Feedback limitations in nonlinear systems: from Bode integrals to cheap controlPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Fundamental Limitations in Filtering and ControlPublished by Springer Nature ,1997
- Constructive Nonlinear ControlPublished by Springer Nature ,1997
- Singular perturbations and input-to-state stabilityIEEE Transactions on Automatic Control, 1996
- Nonlinear Control SystemsPublished by Springer Nature ,1995
- Performance limitations of non-minimum phase systems in the servomechanism problemAutomatica, 1993
- Right half plane poles and zeros and design tradeoffs in feedback systemsIEEE Transactions on Automatic Control, 1985
- Quadratic-type Lyapunov functions for singularly perturbed systemsIEEE Transactions on Automatic Control, 1984
- Cheap control of the time-invariant regulatorApplied Mathematics & Optimization, 1975