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Robust $H^\infty$ control of an uncertain system via a stable decentralized output feedback controller
Kybernetika, Tome 45 (2009) no. 1, pp. 101-120 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 93A14, 93B35, 93B36, 93B50, 93E20
Keywords: robust control; decentralized control; $H^{\infty}$ control 
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Petersen, Ian R. Robust $H^\infty$ control of an uncertain system via a stable decentralized output feedback controller. Kybernetika, Tome 45 (2009) no. 1, pp. 101-120. http://geodesic.mathdoc.fr/item/KYB_2009_45_1_a7/

[1] T. Basar and P. Bernhard: ${H}^{\infty }$-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Birkhäuser, Boston 1991. | MR

[2] D. U. Campos-Delgado and K. Zhou: ${H}_\infty $ strong stabilization. IEEE Trans. Automat. Control 47 (2001), 12, 1968–1972. | MR

[3] Y.-S. Chou, T.-Z. Wu, and J.-L. Leu: On strong stabilization and ${H}^\infty $ strong stabilization problems. In: 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. In: American Control Conference, Minneapolis 2006. | Zbl

[5] I. Petersen: Decentralized state feedback guaranteed cost control of uncertain systems with uncertainty described by integral quadratic constraints. In: 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. | MR

[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. | MR

[8] D. D. Siljak: Decentralized Control of Complex Systems. San Diego, CA: Academic Press, 1991. | MR | Zbl

[9] R. Takahashi, D. Dutra, R. Palhares, and P. Peres: On robust non-fragile static state-feedback controller synthesis. In: 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. | MR

[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.

[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. | MR

[13] M. Zeren and H. Ozbay: On the synthesis of stable ${H}^\infty $ controllers. IEEE Trans. Automat. Control 44 (1999), 2, 431–435. | MR

[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. | MR

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