zbMATH — the first resource for mathematics

Robust \(H^{\infty}\) control of an uncertain system via a stable decentralized output feedback controller. (English) Zbl 1158.93328
Summary: This paper presents a procedure for constructing a stable decentralized output feedback controller for a class of uncertain systems in which the uncertainty is described by Integral Quadratic Constraints. The controller is constructed to solve a problem of robust \(H^\infty\) control. The proposed procedure involves solving a set of algebraic Riccati equations of the \(H^\infty\) control type which are dependent on a number of scaling parameters. By treating the off-diagonal elements of the controller transfer function matrix as uncertainties, a decentralized controller is obtained by taking the block-diagonal part of a non-decentralized stable output feedback controller which solves the robust \(H^\infty\) control problem. This approach to decentralized controller design enables the controller to exploit the coupling between the subsystems of the plant.

93B36 \(H^\infty\)-control
93E20 Optimal stochastic control
93B50 Synthesis problems
93B35 Sensitivity (robustness)
Full Text: Link EuDML
[1] T. Basar and P. Bernhard: \({H}^{\infty }\)-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Birkhäuser, Boston 1991.
[2] D. U. Campos-Delgado and K. Zhou: \({H}_\infty \) strong stabilization. IEEE Trans. Automat. Control 47 (2001), 12, 1968-1972. · Zbl 1012.93024 · doi:10.1109/9.975502
[3] Y.-S. Chou, T.-Z. Wu, and J.-L. Leu: On strong stabilization and \({H}^\infty \) strong stabilization problems. Proc. 42nd IEEE Conference on Decision and Control, Maui 2003, pp. 5155-5160.
[4] I. Petersen: Robust \({H}^{\infty }\) control of an uncertain system via a stable output feedback controller. American Control Conference, Minneapolis 2006. · Zbl 1158.93328 · www.kybernetika.cz · eudml:37664
[5] I. Petersen: Decentralized state feedback guaranteed cost control of uncertain systems with uncertainty described by integral quadratic constraints. American Control Conference, Minneapolis 2006.
[6] I. R. Petersen, V. Ugrinovskii, and A. V. Savkin: Robust Control Design Using \({H}^\infty \) Methods. Springer-Verlag, London 2000. · Zbl 0963.93003
[7] A. V. Savkin and I. R. Petersen: Robust \({H}^\infty \) control of uncertain systems with structured uncertainty. J. Math. Syst. Estim. Control 6 (1996), 4, 339-342. · Zbl 0864.93042
[8] D. D. Siljak: Decentralized Control of Complex Systems. San Diego, CA: Academic Press, 1991. · Zbl 0728.93004
[9] R. Takahashi, D. Dutra, R. Palhares, and P. Peres: On robust non-fragile static state-feedback controller synthesis. Proc. 39th IEEE Conference on Decision and Control, Sydney 2000, pp. 4909-4914.
[10] W.-J. Wang and Y. H. Chen: Decentralized robust control design with insufficient number of controllers. Internat. J. Control 65 (1996), 1015-1030. · Zbl 0874.93007 · doi:10.1080/00207179608921735
[11] J. Yuz and G. C. Goodwin: Loop performance assessment for decentralied control of stable linear systems. European J. Control 9 (2003), 1, 118-132. · Zbl 1293.93067 · doi:10.3166/ejc.9.118-132
[12] A. I. Zecevic and D. D. Siljak: Global low-rank enhancement of decentralized control for large-scale systems. IEEE Trans. Automat. Control 50 (2005), 5, 740-744. · Zbl 1365.93025
[13] M. Zeren and H. Ozbay: On the synthesis of stable \({H}^\infty \) controllers. IEEE Trans. Automat. Control 44 (1999), 2, 431-435. · Zbl 1056.93620 · doi:10.1109/9.746285
[14] G. Zhai, M. Ikeda, and Y. Fujisaki: \({H}^\infty \) controller design: A matrix inequality approach using a homotopy method. Automatica 37 (2001), 4, 565-572. · Zbl 0982.93035 · doi:10.1016/S0005-1098(00)00190-4
[15] K. Zhou, J. Doyle, and K. Glover: Robust and Optimal Control. Prentice-Hall, Upper Saddle River, NJ 1996. · Zbl 0999.49500
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.