A dynamic game approach to the linear H∞ tracking problem

This paper investigates the problem of finite-horizon H_∞ tracking for linear time-varying systems. Three tracking problems are considered, depending on whether the tracking signal is perfectly known in advance, measured on-line, or previewed in a fixed interval of time ahead. No a priori knowledge of a dynamic model for the tracking signal is assumed. A game theory approach to the latter tracking problems is presented. Necessary and sufficient conditions for the existence of a saddle-point equilibrium are determined, and H_∞ tracking controllers for both state and output feedback are derived. Tracking problems for time-invariant systems on infinite-horizon are also analyzed