Robust Stabilization and Observer-Based Stabilization for a Class of Singularly Perturbed Bilinear Systems

Ding-Horng Chen, Chun-Tang Chao and Juing-Shian Chiou
Additional contact information
Ding-Horng Chen: Department of Computer Science and Information Engineering, Southern Taiwan University of Science and Technology, 1, Nan-Tai St., Yongkang District, Tainan 71005, Taiwan
Chun-Tang Chao: Department of Electrical Engineering, Southern Taiwan University of Science and Technology, 1, Nan-Tai St., Yongkang District, Tainan 71005, Taiwan
Juing-Shian Chiou: Department of Electrical Engineering, Southern Taiwan University of Science and Technology, 1, Nan-Tai St., Yongkang District, Tainan 71005, Taiwan

Mathematics, 2021, vol. 9, issue 19, 1-11

Abstract: An infinite-bound stabilization of a system modeled as singularly perturbed bilinear systems is examined. First, we present a Lyapunov equation approach for the stabilization of singularly perturbed bilinear systems for all ? ?(0, ?). The method is based on the Lyapunov stability theorem. The state feedback constant gain can be determined from the admissible region of the convex polygon. Secondly, we extend this technique to study the observer and observer-based controller of singularly perturbed bilinear systems for all ? ?(0, ?). Concerning this problem, there are two different methods to design the observer and observer-based controller: one is that the estimator gain can be calculated with known bounded input, the other is that the input gain can be calculated with known observer gain. The main advantage of this approach is that we can preserve the characteristic of the composite controller, i.e., the whole dimensional process can be separated into two subsystems. Moreover, the presented stabilization design ensures the stability for all ? ?(0, ?). A numeral example is given to compare the new ? -bound with that of previous literature.

Keywords: Lyapunov equation; Lyapunov function; observer; observer-based feedback; singularly perturbed bilinear systems; singular perturbation parameter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/19/2380/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/19/2380/ (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:9:y:2021:i:19:p:2380-:d:642787

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 ().