H∞ preview tracking control of retarded state-multiplicative stochastic systems

The problem of infinite-horizon H∞ state-feedback tracking control for linear continuous time-invariant retarded systems with stochastic parameter uncertainties is investigated. Two tracking patterns are considered depending on the nature of the reference signal; that is, whether it is measured online or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in the dynamics matrices for both the retarded and the non-retarded states of the system. The delayed system is transformed via the input-output approach, to an uncertain norm-bounded system. A new method that efficiently yields a min-max strategy to the solution of each of the aforementioned two cases is suggested where, given a specific reference signal, the controller plays against nature, which chooses the maximizing energy-bounded disturbance. The theoretical results are demonstrated by two examples that show the impact of the delay length and the preview length on the system performance.