THE ROBUST H-2 CONTROL PROBLEM - A WORST-CASE DESIGN

This paper deals with robust performance. We are interested in analyzing the worst-case effect of a disturbance system on the H-2 norm of the system. We will give an explicit expression for the worst-case H-2 norm if we let the disturbance system vary over all nonlinear, time-varying and possibly non-causal systems with bounded L2-induced operator norm. We then define an upper bound for this measure, which is equal to the worst-case H-2 norm if the exogenous input is scalar. We do some further analysis on this upper bound and give a method to design controllers which minimize this upper bound over all robustly stabilizing controllers. The latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature.