Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

Sohaira Ahmad, Muhammad Rehan, Anas Ibrar, Muhammad Umair Ali, Amad Zafar and Seong Han Kim ()
Additional contact information
Sohaira Ahmad: Department of Electrical Engineering, Wah Engineering College, University of Wah, Wah Cantt 47040, Pakistan
Muhammad Rehan: Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad 44000, Pakistan
Anas Ibrar: Department of Electrical Engineering, Wah Engineering College, University of Wah, Wah Cantt 47040, Pakistan
Muhammad Umair Ali: Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea
Amad Zafar: Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea
Seong Han Kim: Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea

Mathematics, 2024, vol. 12, issue 9, 1-30

Abstract: This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.

Keywords: estimation-based control; delay-range-dependent (DRD); one-sided Lipschitz; Wirtinger’s inequality; decoupling procedure; input and output delays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/9/1374/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/9/1374/ (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:12:y:2024:i:9:p:1374-:d:1386864

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 ().