D‐Stability analysis for discrete delay systems

Abstract

This paper discusses the D-pole placement problem of discrete time-delay systems where the delay duration can be any positive integer. One sufficient condition is proposed to insure all the closed-loop eigenvalues of discrete delay systems be located inside a specific disk D(α, r). Several criteria are used to retain all the eigenvalues of discrete delay systems with structured or unstructured parametric perturbations inside the same disk. Finally, some illustrative examples are given to demonstrate our results.

Regional Eigenvalue-Clustering Robustness Analysis for Linear Discrete Time-Delay Systems with Both Structured and Unstructured Parameter Uncertainties

“…Thus, in order to get around this difficulty, all the researchers (2) -(9) directly adopted the linear discrete time-delay system (1) instead of the linear augmented discrete system (3) to develop computationally simple conditions to analyze the robustness problem of eigenvalue-clustering inside a specified region for the linear discrete time-delay system with structured (elemental) parameter uncertainties. Note that the results proposed by Hsieh et al (7), (8) can be applied to analyze the robustness problem of eigenvalue-clustering inside a specified region which may be allowed to be any shape, whereas the results given by Wang and Wang (2), (3) , Trinh and Aldeen (4) , Shyu and Liaw (5) , Chang (6) , and Chen et al (9) can only be applied to analyze the robustness problem of eigenvalueclustering within a specified circular region. For the case of eigenvalue-clustering in a circular region, the sufficient condition proposed by Hsieh et al (7), (8) is shown to be less conservative than those proposed by Wang and Wang (2), (3) , Trinh and Aldeen (4) , Shyu and Liaw (5) , and Chang (6) ; besides, it can be seen that the sufficient condition proposed by Hsieh et al (7), (8) is the generalized version of the results given by Chen et al (9) On the other hand, it is well known that an approximate system model is always used in practice and sometimes the approximation error should be covered by introducing both structured (elemental) and unstructured (norm-bounded) parameter uncertainties in control system analysis and design (10) .…”