Systems with Multiplicative Noise: Stationary output-feedback Tracking with preview

The problem of stationary H_infin output-feedback tracking for linear discrete-time systems with stochastic state-multiplicative parameter uncertainties is investigated. We consider two tracking patterns depending on the nature of the reference signal i.e: whether it is 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 two 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 disturbance. The problems are solved by applying a special Lyapunov function which leads to an LMI based tractable solution. The theory developed is demonstrated by a simple example