Convex methods for robust H-2 analysis of continuous-time systems

This paper treats the robust H-2 performance question of evaluating the rej ection of continuous-time white noise, in the worst case over structured un certainty in the system. A frequency domain convex condition for robust H-2 analysis is presented, with analogous properties as in the discrete-time c ase. In particular, necessary and sufficient results are obtained introduci ng a continuous-time version of the methodology of set descriptions of whit e noise. In addition, a state-space test in terms of linear matrix inequali ties is developed for the robust H-2 problem in the case of constant uncert ainty scalings, which apply to nonlinear or time-varying uncertainty. Thus the problem is rendered finite dimensional in the same situation in which r obust H-infinity analysis is finite dimensional.