Gain-Scheduled Output-Feedback Controllers Using Inexactly Measured Scheduling Parameters for Linear Parametrically Affine Systems

摘要

This note considers the design problem of Gain-Scheduled (GS) controllers for Linear Parameter-Varying (LPV) systems whose state-space matrices are supposed to be parametrically affine with some mild constraints. To be precise, we consider two types of GS controllers, GS H_(2) and GS H_(infinity) controllers. The controllers to be designed are supposed to have parametrically affine state-space matrices. In sharp contrast to conventional GS controller design methods, the scheduling parameters are supposed to be inexactly measured. Using parameter-independent Lyapunov functions, in which some conservatism is admitted, we give sufficient conditions for designing GS H_(2) and GS H_(infinity) output-feedback controllers which are robust against measurement errors of the measured scheduling parameters. The proposed methods are formulated in terms of parametrically affine Linear Matrix Inequalities (LMIs) with single line search parameters. The methods recover the design methods of conventional GS output-feedback controllers, in which scheduling parameters are supposed to be exactly measured, with an appropriate choice of the line search parameters. A simple numerical example is included to illustrate our results.