Linear parameter-varying descriptions of nonlinear systems

Recent methods for gain scheduling controller design based on linear parameter-varying (LPV) systems offer a systematic way to obtain a nonlinear controller. However, the non-unique LPV description of the nonlinear system is essential for the performance of the design. In this paper, two approaches to obtain LPV descriptions are presented. The objective of the approaches is to obtain a closer relationship between the LPV system and the nonlinear system, by minimizing the influence of variations in the parameters. In contrast to earlier approaches, the problem of finding an LPV description is separated from the analysis/synthesis part, resulting in a (convex) linear matrix inequality. An illustrating example indicates the potential of the approaches.