Abstract
In this paper a discrete-time static H ∞ loop shaping control method for linear parameter-varying (LPV) systems is presented. The formulation aims to find a static parameter dependent stabilizing controller which yields guaranteed performance. Using quadratic H ∞ performance, a set of sufficient conditions is provided in a two-step LMI (Linear Matrix Inequality) approach. The first step consists in an extension of the left coprime factorization for discrete-time LPV systems, in which a particular H ∞ filtering problem is solved. In the second step, sufficient conditions for the solution of the static H ∞ loop shaping control problem are provided. Besides considering parameter dependency, these conditions also include nonparametric uncertainties, resulting in more robust closed-loop systems. The effectiveness of the method is illustrated with a numerical example.
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