Open Access Open Access  Restricted Access Subscription or Fee Access

Application of Double Integral Inequality for the Stability Analysis of the Singular Time-Varying Delay System


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/iremos.v15i3.21680

Abstract


This paper aims to establish and analyze the stability of continuous-time linear descriptor systems with a time-varying delay, based on the famous method Lyapunov KRASOVSKI function and the Linear Matrix Inequality (LMI) technique. The founded theorem, not only allows the stability, but also the admissibility, so that the regularity and the impulse free of the studied descriptor system.  The established criterion has been met using a neutral approach, which is the system transformation that checks singular time delayed system stability via a less complicated computation. Additionally to this new form, a major integral inequality lemma has also been used, due to its conservative results. The novelty of this idea is represented in the exploitation of the new double integral inequality proposed, in the admissibility analysis of singular time-delayed system via a neutral approach, which has been used to deliver an alternative delay dependent criterion in term of (LMI). The purpose of this idea is to check this admissibility of the said system through linear matrix inequality founded by programming it on the software numeric computing platform MATLAB. The originality of this article has been obtained by the combination of the double inequality technique and the neutral approach. At the end of this article, a numerical example has been provided using the LMI toolbox, in order to prove the validity and the efficiency of the proposed method. A comparison table will be presented to show the developed results in some other works compared with the proposed theorem, noting that the simulations of this example have been also performed in the MATLAB environment.
Copyright © 2022 Praise Worthy Prize - All rights reserved.

Keywords


Double Integral Inequality; Lyapunov Krasovski; Linear Matrix Inequality; Neutral Approach; Stability

Full Text:

PDF


References


Barra, A., Ouadi, H., Giri, F. et al. Sensorless Nonlinear Control of Wind Energy Systems with Doubly Fed Induction Generator. J Control Autom Electr Syst 27, 562-578 (2016).
https://doi.org/10.1007/s40313-016-0263-1

Li, Yan, Tingting Qiu, and Yuehai Yang. Delay-dependent Stability Criteria for Linear Systems with Two Additive Time-varying Delays. International Journal of Control, Automation and Systems 20.2 (2022).
https://doi.org/10.1007/s12555-020-0344-6

A. Hmamed, H. El Aiss and A. EL Hajjaji, Stability analysis of linear systems with time varying delay: An input output approach, 54th IEEE Conference on Decision and Control (CDC), 2015, pp. 1756-1761, (2015).
https://doi.org/10.1109/CDC.2015.7402464

L. Dai, Singular Control Systems, USA, Springer-Verlag, New York, (1989).
https://doi.org/10.1007/BFb0002475

Sun, M., Zhuang, G., Xia, J., & Chen, G.H∞ dynamic output feedback control for time-varying delay singular Markovian jump systems based on variable elimination technique. Nonlinear Dynamics, 1-11, (2022).
https://doi.org/10.1007/s11071-021-07187-4

Liu Z.Y, Lin C., Chen B, Admissibility analysis for linear singular systems with time-varying delays via neutral system approach, ISA Transactions, 61,141-146,(2016).
https://doi.org/10.1016/j.isatra.2015.12.019

S. Ma, C. Zhang, S. Zhu, Robust stability for discrete-time uncertain singular Markov jump systems with actuator saturation, IET Control Theory and Applications, 5, (2) ,(2011).
https://doi.org/10.1049/iet-cta.2010.0057

Chen, G., Zheng, M., Yang, S., & Li, L. Admissibility Analysis of a Sampled-Data Singular System Based on the Input Delay Approach. Complexity, (2022).
https://doi.org/10.1155/2022/3151620

Jin-Hoon Kim, Further improvement of Jensen inequality and application to stability of time-delayed systems, Automatica, Volume 64,Pages 121-125, (2016).
https://doi.org/10.1016/j.automatica.2015.08.025

P. Balasubramaniam, R. Krishnasamy, R. Rakkiyappan, Delay-dependent stability criterion for a class of non-linear singular Markovian jump systems with mode-dependent interval time-varying delays. Commun Nonlinear Sci Numer Simulat, 9,(17), 3612-3627, (2012).
https://doi.org/10.1016/j.cnsns.2012.01.003

Zhou-Yang Liu, Chong Lin, Bing Chen, A neutral system approach to stability of singular time-delay systems, Journal of the Franklin Institute, Volume 351, Issue 10, Pages 4939-4948,(2014).
https://doi.org/10.1016/j.jfranklin.2014.08.007

Shahbazzadeh, Majid, and Seyed Jalil Sadati. Delay-Dependent Stabilization of Time-Delay Systems with Nonlinear Perturbations. Circuits, Systems, and Signal Processing 41.2, 684-699,(2022).
https://doi.org/10.1007/s00034-021-01810-w

X. Sun, Q. L. Zhang, C. Y. Yang, Z. Su, Y. Y. Shao, An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems, International Journal of Automation and Computing, (2010).
https://doi.org/10.1007/s11633-010-0205-5

Wu Z.G., Park J.H., Su H.Y., J. Chu, Reliable passive control for singular systems with time-varying delays, J. Process Control, 23 (8) (2013).
https://doi.org/10.1016/j.jprocont.2013.07.009

Liu, X., & Shi, K., Further results on stability analysis of time-varying delay systems via novel integral inequalities and improved Lyapunov-Krasovskii functionals. AIMS Mathematics, 7(2), 1873-1895,(2022)..
https://doi.org/10.3934/math.2022108

Fu, X., Sheng, Z., Lin, C., & Chen, B. New results on admissibility and dissipativity analysis of descriptor time-delay systems. Applied Mathematics and Computation, (2022).
https://doi.org/10.1016/j.amc.2021.126860

Xing, Shuangyun, et al., H∞ Control for Stochastic Singular Systems With Time-Varying Delays via Sampled-Data Controller. IEEE Transactions on Cybernetics (2022).
https://doi.org/10.1109/TCYB.2022.3168273

MyeongJin Park, OhMin Kwon, Ju H. Park, SangMoon Lee, EunJong Cha, Stability of time-delay systems via Wirtinger-based double integral inequality, Automatica, Volume 55, Pages 204-208, (2015).
https://doi.org/10.1016/j.automatica.2015.03.010

Xing, Shuangyun, et al., H∞ Control for Stochastic Singular Systems With Time-Varying Delays via Sampled-Data Controller. IEEE Transactions on Cybernetics (2022).
https://doi.org/10.1109/TCYB.2022.3168273

Nan Zhao, Chong Lin, Bing Chen, Qing-Guo Wang n A new double integral inequality and application to stability test for time-delay systems, Applied Mathematics Letters, Volume 65, Pages 26-31, (2017).
https://doi.org/10.1016/j.aml.2016.09.019

El Haouti, K., Chaibi, N., & Amoumou, A. The Employment of Neutral Approach for Linear Singular System Stability Study with Additive Time Varying Delays. Applied Mathematical Sciences, 14(8), 383-392, (2020).
https://doi.org/10.12988/ams.2020.914208

Shahbazzadeh, M., & Sadati, S. J.Further results on delay-dependent state feedback $$ H_infty $$ H∞ control of linear parameter varying time-delay systems. International Journal of Dynamics and Control, (2022).
https://doi.org/10.1007/s40435-022-00924-6

Abu Mallouh, M., Abdelhafez, E., Alajlouni, S., Salah, M., Battery Electric Vehicle Powertrain Modeling, Simulation, and Performance Analysis, (2021) International Review on Modelling and Simulations (IREMOS), 14 (6), pp. 466-475.
https://doi.org/10.15866/iremos.v14i6.21088

Nan Zhao, Chong Lin, Bing Chen, Qing-Guo Wang, A new double integral inequality and application to stability test for time-delay systems, Applied Mathematics Letters, Volume 65,(2017).
https://doi.org/10.1016/j.aml.2016.09.019

Kahouli, A., Guesmi, T., Hadj Abdallah, H., Abderrazak, O., Fuzzy Control Approach for Monomachine Power Systems, (2019) International Journal on Engineering Applications (IREA), 7 (5), pp. 179-187.
https://doi.org/10.15866/irea.v7i5.18408


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize