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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)
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[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
[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
[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
[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
[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
[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
[15] K. Zhou, J. Doyle, and K. Glover: Robust and Optimal Control. Prentice-Hall, Upper Saddle River, NJ 1996. · Zbl 0999.49500
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