H∞ Output-feedback Tracking with Preview of State-multiplicative Noise Systems

The problem of finite-horizon H∞ output-feedback tracking for linear 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, using an expected value of the standard performance index over the stochastic parameters, based on the state-feedback tracking control solution and a specially devised bounded real lemma for state-multiplicative systems with tracking signal.