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 H 2 -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 H 2 -optimal system are formulated, which are important for practical applications.