Exponential stability of LPV systems with guaranteed convergence rate and L2 gain. (14th May 2010)

• Record Type: Journal Article
• Authors: Soliman, M.; Emara, H.; Elshafei, A.; Bahgat, A.; , H.M. Soliman
• Is Part Of: International journal of modelling, identification and control. Volume 9:Number 4(2010)
• Page Start: 359
• Page End: 369
• Publication Date: 2010-05-14
• Subjects: LPV systems -- robust control -- polytopic systems -- linear matrix inequality -- LMI -- feedback control -- linear parameter varying systems -- bilinear matrix inequality -- convergence rates; Engineering -- Methodology -- Periodicals; Science -- Methodology -- Periodicals; 001.42
• Languages: English
• ISSNs: 1746-6172

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.