Robust control design for ellipsoidal plant set

M. Lau, S. Boyd, R. Kosut, and G. Franklin

Proceedings IEEE Conference on Decision and Control, Brighton, U.K, 1:291-296, December 1991.

Presents a control design method for continuous-time plants whose uncertain parameters in the output matrix are only known to lie in an ellipsoidal set. The desired control is chosen to minimize the maximum linear quadratic regulator (LQR) cost from all the plants with parameters in the given set. Although no particular form is assumed for the minimax control, it turns out that it is the LQR control for one of the plants in the set, the worst-case plant. By defining an appropriate mapping, which maps an element from the given ellipsoidal set to an element of the same set, the existence of this worst-case plant is proved. A simple heuristic algorithm to compute the worst-case plant is also given.