-optimisation and fixed poles of multivariable sampled-data systems with delay

Abstract

Using the parametric transfer matrix (PTM) of sampled-data (SD) systems with pure time delay, the paper generalises the polynomial method for solving the -optimisation problem to the multiple-input multiple-output (MIMO) case. The generalisation is not only a formal act, because in the MIMO case, the PTM method leads to a minimisation problem for a singular quadratic functional, which is connected with honest technical difficulties. Therefore, the paper introduces a special transformation to overcome these difficulties. Some general properties of -optimal SD systems with delay are investigated. Notice that there always exists a subset of so-called fixed poles, which is responsible for a principal performance restriction of the -optimal control loop.