An Upper Bound for Finite - Horizon H 2 Performance ofUncertain

A key step in robust H 2 control synthesis for uncertain systems is the development of an upper bound on the H 2 cost function over a given uncertainty set. This paper considers the development of an upper bound on a nite-horizon H 2 cost functional over an assumed uncertainty set using a parameter-dependent bounding function approach. First, a generic upper bound is developed by bounding the uncertain terms in a Lyapunov equation. The bounding function is then assigned a speciic structure using the Popov-Tsypkin multiplier. This results in a nite-horizon cost bound that is a function of the solution of a diierence Lyapunov equation. The results can be applied to nite-horizon robust H 2 control synthesis and analysis for linear discrete-time uncertain systems.