Open AccessOn the poles of two‐time‐scale systems
Author(s) -
Shao Zhenhua
Publication year - 2023
Publication title -
the journal of engineering
Language(s) - English
Resource type - Journals
ISSN - 2051-3305
DOI - 10.1049/tje2.12209
Subject(s) - lti system theory , linear system , mathematics , control theory (sociology) , invariant (physics) , order (exchange) , scale (ratio) , upper and lower bounds , mathematical analysis , computer science , physics , control (management) , mathematical physics , quantum mechanics , artificial intelligence , finance , economics
In this note, the authors will study how the poles of a linear time‐invariant singularly perturbed system are varied versus singular parameter ε, where the poles of the slow and fast subsystems are assumed to be placed in the prescribed regions. An explicitε $\ \varepsilon $ bound is derived such that the poles of the original full order system remain in these regions. Finally, two examples are illustrated to show the applications of the proposed results.