Decentralized robust H∞ output feedback control for value bounded uncertain large-scale interconnected systems
In this paper, decentralized robust H∞ output feedback control problem for large-scale interconnected system with value bounded uncertainties in the state, control input and interconnection matrices is investigated. A new bounded real lemma for the large-scale interconnected systems is derived by Lyapunov stability theory and linear matrix inequality method. Based on the new bounded real lemma, a sufficient condition expressed as matrix inequalities for the existence of a decentralized robust H∞ output feedback controller is obtained. The controller which enables the closed-loop large-scale system robust stable and satisfies the given H∞ performance is designed through a homotopy iterative method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
KeywordsDecentralized robust H∞ control homotopy iterative method non-linear matrix inequality (NLMI) output feedback value bounded uncertainty
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- V. A. Ugrinovskii, I. R. Petersen, A. V. Savkin, and E. Y. Ugrinovskaya, “Decentralized state-feedback stabilization and robust control of uncertain largescale systems with integrally constrained interconnections,” Systems & Control Letters, vol. 40, no. 2, pp. 107–119, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
- C. W. Cheng, “Decentralized robust H∞ control for uncertain delay large-scale systems,” Acta Automatica Sinica (in Chinese), vol. 27, no. 3, pp. 361–366, 2001.Google Scholar
- X. Z. Liu, D. M. Georgi, Y. W. Jing, and S. Y. Zhang, “Robust decentralized stabilization for large-scale systems with multiple time-varying delays and nonlinear uncertainties,” Proc. IEEE conf. Control Applications, Istanbul, pp. 1323–1326, 2003.Google Scholar
- G. Pujol, F. Pozo, J. Rodellar, and J. M. Rossell, “Design of reliable output feedback control for uncertain interconnected systems using LMI,” Proc. 13th IEEE Mediterranean Conf. Control and Automation, Cyprus, pp. 1275–1280, 2005.Google Scholar
- N. Chen, M. Ikeda, and W. H. Gui, “Design of H∞ control of interconnected systems: a homotopy method,” International Journal of Control, Automation, and Systems, vol. 3, no. 2, pp. 143–151, 2005.Google Scholar
- Y. Wang, D. S. Bernstein, and L. T. Watson, “Probability-one homotopy algorithms for solving the coupled Lyapunov equations arising in reducedorder H2/H∞ modeling, estimation, and control,” Applied Mathematics and Computation, vol. 123, no. 2, pp. 155–185, 2001.zbMATHCrossRefMathSciNetGoogle Scholar