An upper bound for finite-horizon H2 performance of uncertain systems

A key step in robust H₂ control synthesis for uncertain systems is the development of an upper bound on the H₂ cost function over a given uncertainty set. This paper considers the development of an upper bound on a finite-horizon H₂ 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 specific structure using the Popov-Tsypkin multiplier. This results in a finite-horizon cost bound that is a function of the solution of a difference Lyapunov equation. The results can be applied to finite-horizon robust H₂ control synthesis and analysis for linear discrete-time uncertain systems