Gain-Scheduled state-feedback controllers using inexactly measured scheduling parameters: H<inf>2</inf> and H<inf>∞</inf> problems

Abstract

In this note, we address two design problems for Linear Parameter-Varying (LPV) systems; Gain-Scheduled (GS) H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> state-feedback controller design and GS H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state-feedback controller design. In sharp contrast to the methods in the literature, the scheduling parameters are supposed to be inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent state-space matrices, and the controllers to be designed are supposed to be rationally parameter-dependent. Using a parametrically affine matrix, which is the inverse of Lyapunov variable, we give formulations for the design of GS H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state-feedback controllers which are robust against the uncertainties in the measured scheduling parameters, in terms of parametrically affine Linear Matrix Inequalities (LMIs). As a special case, our methods include robust controller design using constant Lyapunov variables. Simple numerical examples are included to illustrate our results.