Parametric Transfer Matrices for Sampled-Data Control Systems with Linear Continuous Periodic Process and Control Delay

Abstract

For the class of multi-input multi-output systems being composed of a linear continuous periodic (LCP) process, pure delay, and a digital controller, the paper provides closed expressions for the parametric transfer matrix (PTM), even for the difficult, but practically important case, when the external excitations act on continuous system parts. In the same way as ordinary transfer matrices in the linear time-invariant (LTI) case, the PTM for LCP systems is a fundamental concept for analysis and design of those systems. The properties of the constructed parametric transfer matrices as functions of the real parameter and the complex variable are investigated. These properties are similar to those from ordinary transfer matrices, so that the PTM after some modifications, can be applied with similar tools. Moreover, formulae are derived that are appropriate for the practical computation of the PTM. An example demonstrates, how the formulae can be handled.