Mixed $H_2/H_\infty$ control in a stochastic framework

This paper deals with a mixture of H_2 and H_\infty. We have two inputs and one output. One input signal is a white noise stochastic process, and represents errors e.g. resulting from measurement noise. The other input has a more deterministic character. If one has a reference signal (e.g. a step) as input one can not model this as white noise, but it fits nicely into this new class of inputs. The objective is to minimize the effect of these exogenuous signals on the output ofthe system. We define a cost function which enables us to combine the structural difference between these two exogenuous inputs. The analysis of this function leads to a standard H_\infty Riccati equation. We will motivate this cost function by looking at two theoretical applications: the derivation of robust performance bounds and a tracking problem.