An Improved Approach to Design Linear Parameter-Varying Controllers subject to Uncertain Parameter Measurements

This paper presents an improved approach for the design of linear parameter-varying controllers subject to uncertain parameter measurements. Specifically, we assume both additive and multiplicative uncertainty on the measured parameter, such that the parameter and its measurement assume values in a nonconvex domain. Closed-loop stability and performance is guaranteed by finding a parameter-dependent (PD) Lyapunov matrix such that a PD linear matrix inequality (LMI) is feasible on this nonconvex domain. We propose to express the nonconvex domain as the image of a polynomial spline, such that the PD LMI is equivalently expressed as a PD LMI on a hyperrectangle. To solve the resulting infinite-dimensional LMI problem, we propose a novel relaxation technique that exploits the properties of B-spline basis functions. An extensive numerical example demonstrates the merits of our approach compared to the state of the art. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.