# Article

 Title: Robust $H^\infty$ control of an uncertain system via a stable decentralized output feedback controller (English) Author: Petersen, Ian R. Language: English Journal: Kybernetika ISSN: 0023-5954 Volume: 45 Issue: 1 Year: 2009 Pages: 101-120 Summary lang: English . Category: math . 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. (English) Keyword: robust control Keyword: decentralized control Keyword: $H^{\infty}$ control MSC: 93A14 MSC: 93B35 MSC: 93B36 MSC: 93B50 MSC: 93E20 idZBL: Zbl 1158.93328 idMR: MR2489583 . Date available: 2010-06-02T18:21:52Z Last updated: 2012-06-06 Stable URL: http://hdl.handle.net/10338.dmlcz/140006 . Reference: [1] T. Basar and P. Bernhard: ${H}^{\infty }$-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach.Birkhäuser, Boston 1991. MR 1096294 Reference: [2] D. U. Campos-Delgado and K. Zhou: ${H}_\infty$ strong stabilization.IEEE Trans. Automat. Control 47 (2001), 12, 1968–1972. MR 1878223 Reference: [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. Reference: [4] I. Petersen: Robust ${H}^{\infty }$ control of an uncertain system via a stable output feedback controller.In: American Control Conference, Minneapolis 2006. Zbl 1158.93328 Reference: [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. Reference: [6] I. R. Petersen, V. Ugrinovskii, and A. V. Savkin: Robust Control Design Using ${H}^\infty$ Methods.Springer-Verlag, London 2000. MR 1834840 Reference: [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 1653087 Reference: [8] D. D. Siljak: Decentralized Control of Complex Systems.San Diego, CA: Academic Press, 1991. Zbl 0728.93004, MR 1086632 Reference: [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. Reference: [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 1662192 Reference: [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. Reference: [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 2141585 Reference: [13] M. Zeren and H. Ozbay: On the synthesis of stable ${H}^\infty$ controllers.IEEE Trans. Automat. Control 44 (1999), 2, 431–435. MR 1668932 Reference: [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 1832530 Reference: [15] K. Zhou, J. Doyle, and K. Glover: Robust and Optimal Control.Prentice-Hall, Upper Saddle River, NJ 1996. .

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