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

Abstract In this paper we investigate the closed-loop performance of a sampled-data control system by utilizing exact discretization techniques. In particular, for an H 2 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 → 0, and slow sampling near open loop, h → ∞. 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.

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