Gain-Scheduled H<inf>∞</inf> filters using inexactly measured scheduling parameters

Abstract

This note addresses the design problem of Gain- Scheduled (GS) H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters for Linear Parameter-Varying (LPV) systems under the condition that the scheduling parameters are inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent state-space matrices, and the filters to be designed are supposed to have rationally parameter-dependent state-space matrices. Using structured polynomially Parameter-Dependent Lyapunov Functions (PDLFs), we give a formulation for the design of GS H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters which are robust against the uncertainties in the measured scheduling parameters in terms of parametrically affine Linear Matrix Inequalities (LMIs). Our method encompasses a design method for robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters as a special case. A simple numerical example is included to illustrate our results.