On the Principal Relative Degree for Linear Time-Delay Systems with Applications to Tracking, Disturbance Decoupling, and Model Matching

Abstract.

The generalization and application of the notion of relative degree for a class of linear systems with general state delays are studied in this paper. First, novel notions, referred to as the principal relative degree (P-relative degree) and regular P-relative degree, are introduced, which extend the notion of type-II relative degree and take the sensitivity of the relative degree to small delay perturbations into account. Then the existence of the regular P-relative degree under output transformations is investigated. Necessary and sufficient conditions for the existence of an output transformation are established by using rank identities, such that the transformed system has a regular P-relative degree. In addition, an algorithm to construct such a transformation is designed. Finally, the regular P-relative degree is applied to solving a batch of vital control problems, including the output tracking problem, the disturbance decoupling problem, and the (asymptotic) model matching problem. Some numerical examples are given to illustrate the validity of theoretical results.