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

doi:10.1016/0005-1098(95)98492-O

Automatica

Volume 31, Issue 4, April 1995, Pages 617-620

https://doi.org/10.1016/0005-1098(95)98492-O Get rights and content

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 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 → 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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Citation Excerpt :
As a by-product we show that for h→0 the conditions coincide with the necessary and sufficient conditions for the continuous-time stabilization. Such convergence in H2 framework and related results were proved by Mikheev et al. (1988), Chen and Francis (1991), Fridman (1992), Osborn and Bernstein (1995), Trentelman and Stoorvogel (1995) and Oishi (1997). From A1 it follows that τ(t)⩽h since τ(t)⩽tk+1−tk.
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^☆: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor F. Delebecque under the direction of Editor R. F. Curtain.

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

Abstract

Syst. Control Lett.

Syst. Control Lett.

Automatica

The optimal projection equations for fixed-order sampled-data dynamic compensation with computational delay

IEEE Trans. Autom. Control

Intersample variances in discrete minimum variance control

IEEE Trans. Autom. Control

Optimal linear regulators: the discrete time case

IEEE Trans. Autom. Control

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