An exact treatment of the achievable closed-loop H2 performance of sampled-data controllers: from continuous-time to open-loop

In this paper we investigate the closed-loop performance of a sampled-data control system by utilizing exact discretization techniques. In particular, for an H2 performance measure we give exact expressions for the closed-loop cost for a given sample interval h. After applying discrete-time LQG synthesis to the sampled-data system, the achievable performance is evaluated for fast sampling near continuous time, h +O, and slow sampling near open loop, h-t m. Connections between the continuous-time Riccati equation for the analog control system and the discrete-time Riccati equation for the sampled-data system are investigated. Finally, several numerical examples are given to illustrate the convergence from sampled-data control to continuous-time control and open-loop.