[工程科技]TU Delft.pdf

PAPER SUBMITTED TO INTERNATIONAL JOURNAL OF CONTROL H ∞ Output Feedback Control for Linear, Discrete Time-Varying Systems via the Bounded Real Lemma Jacquelien Scherpen, Michel Verhaegen Revised version, May 1995, November 1995 TU Delft Department of Electrical Engineering Control Laboratory P.O. Box 5031, 2600 GA Delft, The Netherlands Tel. (31-15) 2 78 57 68 Fax. (31-15) 2 62 67 38 Delft University of Technology e-mail: J.M.A.Scherpen@et.tudelft.nl M.H.G.Verhaegen@et.tudelft.nl Abstract In this paper we develop a solution to the discrete-time H∞ output feedback control problem for Linear Time-Varying (LTV) systems. The solution is developed along the strategy set up in [Doyle et. al. 1989] and the main ingredient in its derivation is the extension of the well-known bounded real lemma to a (discrete) time-varying context, developed in [van der Veen and Verhaegen 1995]. This approach contributes to the conceptual simplicity, and hence to the accessibility, of the solution. Apart from that, we treat the infinite-horizon case for LTV sy stem of non-uniform state dimension, and vary- ing input and output dimension. Both situations can easily occur in practice, e.g. in multirate sampled data control systems. The algorithm that can be derived from the solution presented is then applied to the H∞ output feedback of a dynamical system changing from one operation point in its operation envelope to another. Keywords Positive real lemma, discrete time-varying system, H∞ control, Riccati equations. 1. INTRODUCTION The major part of the research