Discrete-time static H∞ loop shaping control for LPV systems

• Published in: 2017 25th Mediterranean Conference on Control and Automation (MED) pp. 619 - 624
• Main Authors: Pereira, Renan L., Kienitz, Karl H., Guaracy, Fernando H. D.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-07-2017
• Subjects: Closed loop systems; Observers; Output feedback; Robustness; Symmetric matrices; Uncertainty
• ISSN: 2473-3504
• DOI: 10.1109/MED.2017.7984186

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.