ℋ₂-optimisation of MIMO sampled-data systems with pure time-delays

Abstract

This article considers the digital control of a MIMO continuous-time process, when we have time-delays at different locations in the control loop. The controller has to be causal (realisable) and stabilising. Under these restrictions, we search for the controller ensuring the minimal ℋ₂-norm of the closed loop. Using the parametric transfer function concept, a constructive method for the solution of this problem is provided. On the basis of these results, a number of characteristic properties of the closed ℋ₂-optimal system are formulated, which are important for practical applications.

Keywords:

• sampled-data systems
• MIMO
• time-delays
• stochastic distrubances
• transfer functions

Acknowledgements

The authors are grateful to Dr Sc. Techn. K.Y. Polyakov, who has calculated the example and gave a number of helpful comments to the content of this article. The authors would also like to thank the anonymous reviewer for helpful comments, and the German Science Foundation (DFG) for financial support.