Robust state-feedback control of uncertain LPV systems: An LMI-based approach

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∞ and the H2 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.