Quadratic games and H∞-type problems for time varying systems

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Abstract
H∞-type control problems with state feedback are considered for time varying systems. First, general quadratic differential games are studied and then the relationship between H∞-problems and differential games is clarified. A necessary and sufficient condition for the existence of a stabilizing controller, such that the norm of the operator from the disturbance to the output is less than a prescribed number, is given in terms of a Riccati equation. Earlier results on time invariant systems are found to be special cases of our main results. The finite horizon problem is also studied.