Abstract
In this chapter we bring together the separate threads of synthesis of feedback controllers in the absence of uncertainty, and analysis of uncertain systems, into a common problem involving both uncertainty and control. This problem is represented by the diagram shown in Figure 9.1, where G is the generalized plant as in earlier chapters, but now also describes dependence on system uncertainty. The perturbation Δ belongs to a structured ball, and K represents the controller.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes and references
G. Zames. On the input-output stability of time varying nonlinear feedback systems. Part I: Conditions derived using concepts of loop gain, conicity, and positivity. IEEE Transactions on Automatic Control, 11: 228–238, 1966.
V. M. Popov. On the absolute stability of nonlinear systems of automatic control. Automation and Remote Control, 22: 857–875, 1961.
V. A. Yakubovich. Frequency conditions for the absolute stability of control systems with several nonlinear or linear nonstationary units. Automat. Telemech., pages 5–30, 1967.
C.A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties. Academic Press, 1975.
J.C. Willems. The Analysis of Feedback Systems. MIT Press, 1971.
M. G. Safonov and M. Athans. A multiloop generalization of the circle criterion for stability margin analysis. IEEE Transactions on Automatic Control, 26: 415–422, 1981.
J.S. Shamma. The necessity of the small-gain theorem for time-varying and nonlinear systems. IEEE Transactions on Automatic Control, 36: 1138 1147, 1991.
M. Khammash and J. B. Pearson. Performance robustness of discrete-time systems with structured uncertainty. IEEE Transactions on Automatic Control, 36: 398–412, 1991.
A. Megretski. Necessary and sufficient conditions of stability: A multi-loop generalization of the circle criterion. IEEE Transactions on Automatic Control, 38: 753–756, 1993.
J.S. Shamma. Robust stability with time varying structured uncertainty. IEEE Transactions on Automatic Control, 39: 714–724, 1994.
J. C. Doyle, J. E. Wall, and G. Stein. Performance and robustness analysis for structured uncertainty. In Proc. IEEE Conference on Decision and Control, 1982.
J.C. Doyle. Structured uncertainty in control system design. In Proc. IEEE Conference on Decision and Control, 1985.
M. G. Safonov and R.Y. Chiang. Real/complex K m synthesis without curve fitting. In Control and Dynamic Systems; editor C. T. Leondes. Academic Press, 1993.
A. Packard, K. Zhou, P. Pandey, J. Leonhardson, and G. Balas. Optimal, constant I/O similarity scaling for full-information and state-feedback control problems. Systems and Control Letters, 19: 271–280, 1992.
A. Rantzer and A. Megretski. A convex parameterization of robustly stabilizing controllers. IEEE Transactions on Automatic Control, 39: 1802–1808, 1994.
R. D’Andrea. Generalized £2 synthesis. IEEE Transactions on Automatic Control, 44: 1145–1156, 1999.
G. Zames and J. G. Owen. Duality theory for MIMO robust disturbance rejection. IEEE Transactions on Automatic Control, 38:743–752., 1993.
J. G. Owen and G. Zames. Duality theory for robust disturbance attenuation. Automatica, 29: 695–705, 1993.
M. Mesbahi, M.G. Safonov, and G.P. Papavassilopoulos. Bilinearity and complementarity in robust control. In Recent Advances on LMI Methods in Control; editors L. El Ghaoui, S. Niculescu. SIAM, 1999.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Dullerud, G.E., Paganini, F. (2000). Feedback Control of Uncertain Systems. In: A Course in Robust Control Theory. Texts in Applied Mathematics, vol 36. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3290-0_10
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3290-0_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3189-4
Online ISBN: 978-1-4757-3290-0
eBook Packages: Springer Book Archive