Stability Analysis for Digital Redesign of Discrete-Time Switched Systems Using H ∞ Linear Matrix Inequality

Nien-Tsu Hu ()
Additional contact information
Nien-Tsu Hu: Graduate Institute of Automation Technology, National Taipei University of Technology, Taipei 10608, Taiwan

Mathematics, 2023, vol. 11, issue 11, 1-22

Abstract: In this paper, the stability problem for the digital redesign of discrete-time switched systems using H ∞ linear matrix inequality (LMI) is investigated. We propose the switching time approach for digital redesign between controller work and failure, and this switching time will limit the system output within the system capacity. When the controller fails, the overall system will be unstable. Therefore, if the digital redesign controller is not restored in a certain period of time, the system output will exceed the system capacity. To solve this problem, we propose a switching law to determine the switching time between the stable mode (controller work) and the unstable (controller failure) mode; this will limit the overall system states in the unstable mode. In addition, the digital redesign controller has the advantage of faster tracking. After we propose a discrete-time switching system with stable and unstable modes, we use H ∞ linear matrix inequality (LMI) and Lyapunov functions to prove the stability in detail. Finally, the numerical example illustrates the feasibility of the proposed approach.

Keywords: digital redesign; switched systems; linear matrix inequality; Lyapunov functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/11/2468/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/11/2468/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:11:p:2468-:d:1157317

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().