Gain-Scheduled output-feedback controllers using inexactly measured scheduling parameters

Abstract

This note considers 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> output-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> output-feedback controller design. In sharp contrast to the conventional design methods, the scheduling parameters are supposed to be inexactly measured. The LPV systems are supposed to have parametrically affine state-space matrices with some mild constraints, and the controllers to be designed are also supposed to have parametrically affine state-space matrices. Using parameter-independent Lyapunov functions, we give sufficient conditions for designing GS H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and GS H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> output-feedback controllers, which are robust against the uncertainties in the measured scheduling parameters, in terms of parametrically affine Linear Matrix Inequalities (LMIs) with single line search parameters. Our methods recover the design methods of conventional GS output-feedback controllers with an appropriate choice for the line search parameters. We also give an extension of our methods to robust controller design for LPV systems. A simple numerical example is included to illustrate our results.