Title: Exponential stability of LPV systems with guaranteed convergence rate and L₂ gain

Authors: M. Soliman, H. Emara, A. Elshafei, A. Bahgat, H.M. Soliman

Addresses: Department of Electrical Engineering, Faculty of Engineering, Cairo University, Gamaa Street, Giza 12613, Egypt; Department of Electrical Engineering, Calgary University, Calgary, Canada. ' Department of Electrical Engineering, Faculty of Engineering, Cairo University, Gamaa Street, Giza 12613, Egypt. ' Department of Electrical Engineering, Faculty of Engineering, Cairo University, Gamaa Street, Giza 12613, Egypt. ' Department of Electrical Engineering, Faculty of Engineering, Cairo University, Gamaa Street, Giza 12613, Egypt. ' Department of Electrical Engineering, Faculty of Engineering, Cairo University, Gamaa Street, Giza 12613, Egypt

Abstract: In this paper, the design of observer-based output feedback controller that guarantees exponential stability for polytopic linear parameter varying (LPV) systems is derived in the LMI framework. The problem is first formulated in terms of bilinear matrix inequalities (BMIs) and then sufficient linear matrix inequalities (LMIs) with equality constraint are provided to ensure exponential stability. The convergence rate of the system is also estimated. In the case of structured uncertainty, such as in the case of LPV system, the presented approach achieves less conservative results than that in the case of representing the uncertainty as a norm bounded one. Furthermore, the proposed controller synthesis guarantees many performance criteria such as: 1) the convergence rate of the closed loop system to be greater than certain desired value, 2) the worst case L₂ gain of the closed loop system to be less than certain desired value for all parameter trajectories.

Keywords: LPV systems; robust control; polytopic systems; linear matrix inequality; LMI; feedback control; linear parameter varying systems; bilinear matrix inequality; convergence rates.

DOI: 10.1504/IJMIC.2010.033211

International Journal of Modelling, Identification and Control, 2010 Vol.9 No.4, pp.359 - 369

Published online: 13 May 2010 *

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