Reduced-order ℋ2/ℋ∞ control of discrete-time LPV systems with experimental validation on an overhead crane test setup

This paper presents a numerically attractive approach to design reduced-order multi-objective ℋ₂/ℋ_∞ controllers for discrete-time linear parameter-varying (LPV) systems. The proposed controller synthesis approach relies on an a priori computed polynomially parameter-dependent full-order LPV controller that stabilizes the LPV system for all possible parameter trajectories. This full-order controller is subsequently used in a sufficient linear matrix inequality (LMI) optimization problem for reduced-order ℋ₂/ℋ_∞ LPV synthesis. Pólya relaxations are used to obtain tractable LMI formulations, and a simplicial subdivision of the parameter domain is applied to relieve the numerical burden. Experimental validations on a lab-scale overhead crane with varying cable length illustrate the practical viability of the approach.