Stabilization of a plant with variable operating conditions: Interpolation of more than two representative models

Abstract

Stabilization of a multi-input multi-output plant with variable operating conditions is considered. The plant is described as a linear interpolation of proper stable factorizations of transfer functions defined at representative operating points. In this paper, more than two representative models are considered, in contrast with the case of two representative models, which has been extensively dealt with so far. To stabilize the closed-loop system, a controller being an interpolation of stabilizing controllers for the representative models is employed as well as a fixed controller. The stabilization problems are reduced to certain H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control problems. Sufficient conditions for the existence of controllers and design methods are expressed in terms of LMIs (linear matrix inequalities) in state space.