Robust controller with time specifications for systems with stochastic uncertainties

In this paper, the design of a robust controller for systems with stochastic uncertainties is developed. The main idea is built on the generalized Polynomial Chaos theory, which transforms the stochastic dynamic model to an equivalent higher order deterministic dynamic model. The controller synthesis is formulated over the expanded system, taking in account the desired closed loop performances such as settling time and overshoot. The designed controller is then applied to the nominal and worst-case systems. Simulation results are presented to shed light on the efficiency and performance of the proposed controller.