State-multiplicative noisy systems - H_∞ dynamic output-feedback tracking with preview

The problem of finite-horizon H_∞ outputfeedback tracking control for linear discrete time-varying systems with stochastic state-multiplicative parameter uncertainties is investigated. We consider three tracking patterns depending on the nature of the reference signal i.e : whether it is perfectly known in advance, measured on-line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. For each of the above three cases a solution is found where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy-bounded disturbances. The problems are solved based on a specially devised bounded real lemma for state-multiplicative systems with tracking signals. The finite-horizon case is extended to the stationary one where similar results are achieved.