Robust control of discrete linear systems with ellipsodial uncertainty

In this paper, an H_∞ robust control design technique is developed for unknown discrete linear time-invariant systems subject to a bounded time-varying disturbance. This technique essentially combines two typical procedures of system indentification and H_∞ control design in literature. Once the given system is described as a discrete linear time-invariant system with plant uncertainty through the system identification procedure, a stabilizing H_∞ control is then designed to handle the plant uncertainty. The main challenge in this approach is the treatment of the plant uncertainty typically belonging to an ellipsoidal set, in the existing H_∞ control framework. In this paper, a simple coordination transformation scheme is used to tackle this challenge.