Exponential stability of LPV systems with guaranteed convergence rate and L2 gain (original) (raw)
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Exponential stabilization of LPV systems: An LMI approach
2008 Canadian Conference on Electrical and Computer Engineering, 2008
The design of robust observer-based output feedback controller that guarantees exponential stability for linear parameter varying (LPV) systems is considered in this paper. The synthesis 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 controller parameters are calculated efficiently using convex optimization techniques. The convergence rate of the closed loop system is also estimated. Furthermore, in the case of structured uncertainty, such as in the case of LPV systems, the proposed approach achieves less conservative results than that in the case of representing the uncertainty as a norm bounded one.
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Journal of the Franklin Institute, 2014
In this paper, the problem of designing an LPV state-feedback controller for uncertain LPV systems that can guarantee some desired bounds on the H 1 and the H 2 performances and that satisfies some desired constraints on the closed-loop poles location is considered. In the proposed approach, the vector of varying parameters is used to schedule between uncertain LTI systems. The resulting idea consists in using a double-layer polytopic description so as to take into account both the variability due to the parameter vector and the uncertainty. The first polytopic layer manages the varying parameter and is used to obtain the vertex uncertain systems, where the vertex controllers are designed. The second polytopic layer is built at each vertex system so as to take into account the model uncertainties and add robustness into the design step. Under some assumptions, the problem reduces to finding a solution to a finite number of LMIs, a problem for which efficient solvers are available nowadays. The solution to the multiobjective design problem is found both in the case when a single fixed Lyapunov function is used and when multiple parameter-varying Lyapunov functions are used. The validity and performance of the theoretical results are demonstrated through a numerical example.
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IEE Proceedings - Control Theory and Applications, 2005
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Advances in Difference Equations, 2012
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Automatica, 2007
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