Standardizability of multivariable linear sampled-data systems with delay

Abstract

Due to periodic sampling, linear sampled-data systems are a subclass of linear continuous periodic systems, even in the case, when all other elements are time invariant. Therefore, the well-established methods for LTI systems cannot be applied. Owing to the great practical importance of sampled-data control systems, various approaches for the rigorous description of those systems are known. Moreover, a lot of methods have been developed, that are able to yield rigorous solutions for numerous control and optimization problems. The application of those methods need representations in certain standard forms. Often, it is not clear, whether a given system can be transformed into a standard form or not. The paper considers this question for the standard sampled-data system with delay, for which numerous methods and tools are available, if the system belongs to the subclass with model structure. The paper provides necessary and sufficient conditions for a SD system with delay in standard structure to belong to this important subclass. The proof is given on basis of the parametric transfer matrix concept, which is at present the only one that can handle problems, where both difficulties -sampling and arbitrary time-delay - occur at the same time.