Stabilization of LFT systems

Abstract

The problem of parametrizing all stabilizing controllers for general linear fractional transformation (LFT) systems is studied. The LFT systems can be variously interpreted as multidimensional systems or uncertain systems, and the controller is allowed to have the same dependence on the frequency/uncertainty structure as the plant. For multidimensional systems, this means that the controller is allowed dynamic feedback, while the uncertain system case can be given a gain scheduling interpretation. Both mu and Q stability are considered, although the latter is emphasized. In both cases, the output feedback problem is reduced by a separation argument to two simpler problems, involving the dual problems of full information and full control. For Q stability, these problems can be characterized completely in terms of linear matrix inequalities. In the standard 1D system case with no uncertainty, the results in the present work reduce to the standard parametrization of D.C. Youla, H.A. Jabr and J.J. Bongiorno (1976), although the development appears to be much simpler, and does not require coprime factorizations.

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