Top

Circuits, Systems, and Signal Processing

Published in:

08-07-2024

Finite-Time \(H_\infty \) Control for Time-Delayed Markovian Jump Nonlinear Systems with Parameter Uncertainties and Generally Uncertain Transition Rates

Authors: Chenyang Jiao, Juan Zhou

Published in: Circuits, Systems, and Signal Processing | Issue 10/2024

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper mainly investigates the problem of finite-time \(H_{\infty }\) control for a class of uncertain Markovian jump nonlinear systems (MJNSs) with time-varying delay and generally uncertain transition rates. By constructing the appropriate Lyapunov–Krasovskii functional and free weighting matrices, a novel criterion on finite-time boundedness for the MJNSs with \(H_{\infty }\) performance is derived. We use a special way to deal with the bilinear terms, the mode-dependent state feedback controller is designed to ensure the \(H_{\infty }\) finite-time boundedness of the closed-loop system in the forms of strict linear matrix inequalities. Finally, numerical and practical examples are given to demonstrate the effectiveness of the proposed method.

previous article Output-Based Adaptive Event-Triggered Control of Saturated Systems with Dynamic Anti-Windup Compensator

next article Modeling Source and System Features Through Multi-channel Convolutional Neural Network for Improving Intelligibility Assessment of Dysarthric Speech

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

ATZelektronik

Die Fachzeitschrift ATZelektronik bietet für Entwickler und Entscheider in der Automobil- und Zulieferindustrie qualitativ hochwertige und fundierte Informationen aus dem gesamten Spektrum der Pkw- und Nutzfahrzeug-Elektronik.

Lassen Sie sich jetzt unverbindlich 2 kostenlose Ausgabe zusenden.

inform now

ATZelectronics worldwide

ATZlectronics worldwide is up-to-speed on new trends and developments in automotive electronics on a scientific level with a high depth of information.

Order your 30-days-trial for free and without any commitment.

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

M. Bahreini, J. Zarei, Robust finite-time fault-tolerant control for net-worked control systems with random delays: a Markovian jump system approach. Nonlinear Anal. Hybrid Syst. 36, 393–406 (2020). https://doi.org/10.1016/j.nahs.2020.100873CrossRef

Y. Cao, A. Chandrasekar, T. Radhika, V. Vijayakumar, Input-to-state stability of stochastic Markovian jump genetic regulatory networks. Math. Comput. Simul. 222, 174–187 (2024). https://doi.org/10.1016/j.matcom.2023.08.007MathSciNetCrossRef

A. Chandrasekar, T. Radhika, Q. Zhu, State estimation for genetic regulatory networks with two delay components by using second-order reciprocally convex approach. Neural Process. Lett. 54(1), 327–345 (2022). https://doi.org/10.1007/s11063-021-10633-4CrossRef

Q.Y. Chen, D.B. Tong, W.N. Zhou, Finite-time stochastic boundedness for Markovian jumping systems via the sliding mode control. J. Frankl. Inst. 359(10), 4678–4698 (2022). https://doi.org/10.1016/j.jfranklin.2022.05.005MathSciNetCrossRef

T.W. Chen, J. Wu, L. Wang, Delay-dependent robust stability and \(H_{\infty }\) control for jump linear systems with delays. Syst. Control Lett. 55(11), 939–948 (2006). https://doi.org/10.1016/j.sysconle.2006.06.006MathSciNetCrossRef

H. Fatoorehchi, H. Abolghasemi, R. Rach, Chaos control in the cerium-catalyzed Belousov-Zhabotinsky reaction using recurrence quantification analysis measures. Chaos Solitons Fractals 76, 121–129 (2015). https://doi.org/10.1016/j.chaos.2015.03.019CrossRef

H. Fatoorehchi, H. Abolghasemi, R. Zarghami, Analytical approximate solutions for a general nonlinear resistor-nonlinear capacitor circuit model. Appl. Math. Model. 39(19), 6021–6031 (2015). https://doi.org/10.1016/j.apm.2015.01.038MathSciNetCrossRef

H. Fatoorehchi, H. Abolghasemi, R. Zarghami, R. Rach, Feedback control strategies for a cerium-catalyzed Belousov-Zhabotinsky chemical reaction system. Can. J. Chem. Eng. 93(7), 1212–1221 (2015). https://doi.org/10.1002/cjce.22213CrossRef

H.L. Gao, F.C. Liu, Delay-dependent robust resilient \(H_{\infty }\) control for uncertain singular time-delay system with Markovian jumping parameters. Cluster Comput. 22(3), 6283–6294 (2019). https://doi.org/10.1007/s10586-018-1985-6CrossRef

10.

X.W. Gao, L. Lian, W.H. Qi, Finite-time dissipativity analysis and design for stochastic Markovian jump systems with generally uncertain transition rates and time-varying delay. Trans. Inst. Meas. Control. 39(6), 807–819 (2017). https://doi.org/10.1177/0142331215620465CrossRef

11.

Y.F. Guo, An improved approach to synthesis of Markov jump nonlinear systems with generally uncertain transition rates. Asian J. Control 25(3), 2305–2314 (2023). https://doi.org/10.1002/asjc.2933MathSciNetCrossRef

12.

Y.F. Guo, Z.J. Wang, Stability of Markovian jump systems with generally uncertain transition rates. J. Frankl. Inst. 350(9), 2826–2836 (2013). https://doi.org/10.1016/j.jfranklin.2013.06.013MathSciNetCrossRef

13.

B.E. Haiek, H.E. Aiss, H. Abdelaziz, A.E. Hajjaji, T.E. Houssaine, New approach to robust observer-based control of one-sided lipschitz non-linear systems. IET Control Theory Appl. 13(3), 333–342 (2019). https://doi.org/10.1049/iet-cta.2018.5389MathSciNetCrossRef

14.

L.W. Li, G.H. Yang, Decentralised output feedback control of Markovian jump interconnected systems with unknown interconnections. Int. J. Syst. Sci. 48(9), 1856–1870 (2017). https://doi.org/10.1080/00207721.2017.1291866MathSciNetCrossRef

15.

X.H. Li, W.D. Zhang, D.K. Lu, Stability and stabilization analysis of Markovian jump systems with generally bounded transition probabilities. J. Frankl. Inst. 357(13), 8416–8434 (2020). https://doi.org/10.1016/j.jfranklin.2020.04.013MathSciNetCrossRef

16.

R.Q. Lu, B. Lou, A.K. Xue, Mode-dependent quantised \(H_{\infty }\) filtering for Markovian jump singular system. Int. J. Syst. Sci. 46(10), 1817–1824 (2015). https://doi.org/10.1080/00207721.2013.837539MathSciNetCrossRef

17.

L. Ma, C.Q. Wang, S.H. Ding, L.L. Dong, Integral sliding mode control for stochastic Markovian jump system with time-varying delay. Neurocomputing 179, 118–125 (2016). https://doi.org/10.1016/j.neucom.2015.11.071CrossRef

18.

K.S. Min, B.P. Jin, H.J. Young, Stability and stabilization for discrete-time Markovian jump fuzzy systems with time-varying delays: Partially known transition probabilities case. Int. J. Control Autom. Syst. 11(1), 136–146 (2013). https://doi.org/10.1007/s12555-011-9112-yCrossRef

19.

Y.N. Pan, W.Y. Ji, H.K. Lam, L. Cao, An improved predefined-time adaptive neural control approach for nonlinear multiagent systems. IEEE Trans. Autom. Sci. Eng. (2023). https://doi.org/10.1109/TASE.2023.3324397CrossRef

20.

W.H. Qi, X.W. Gao, Finite-time \(H_{\infty }\) control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity. Int. J. Syst. Sci. 47(2), 500–508 (2016). https://doi.org/10.1080/00207721.2015.1025891MathSciNetCrossRef

21.

W.H. Qi, Y.Y. Zhou, L.H. Zhang, J.D. Cao, J. Cheng, Non-fragile \(H_{\infty }\) SMC for Markovian jump systems in a finite-time. J. Frankl. Inst. 358(9), 4721–4740 (2021). https://doi.org/10.1016/j.jfranklin.2021.04.010CrossRef

22.

T. Radhika, A. Chandrasekar, V. Vijayakumar, Q.X. Zhu, Analysis of Markovian jump stochastic Cohen–Grossberg BAM neural networks with time delays for exponential input-to-state stability. Neural Process. Lett. 55(8), 11055–11072 (2023). https://doi.org/10.1007/s11063-023-11364-4CrossRef

23.

S. Saravanan, M. Syed Ali, H. Alsulami, M.S. Alhodaly, Robust \(H_{\infty }\) filtering for finite-time boundedness of Markovian jump system with distributed time-varying delays. Int. J. Syst. Sci. 51(2), 368–380 (2020). https://doi.org/10.1080/00207721.2020.1716097

24.

F. Shu, M. Li, Q.Z. Huang, J. Wang, Observer-based \(H_{\infty }\) control for Markovian jump systems with time-varying delays and incomplete transition rates. Int. J. Robust Nonlinear Control 28(16), 4772–4789 (2018). https://doi.org/10.1002/rnc.4284MathSciNetCrossRef

25.

G.T. Tian, Finite-time \(H_{\infty }\) control for stochastic Markovian jump systems with time-varying delay and generally uncertain transition rates. Int. J. Syst. Sci. 52(12), 2446–2459 (2021). https://doi.org/10.1080/00207721.2021.1889709MathSciNetCrossRef

26.

D.B. Tong, C. Xu, Q.Y. Chen, W.N. Zhou, Y.H. Xu, Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays. Nonlinear Dyn. 100(2), 1343–1358 (2020). https://doi.org/10.1007/s11071-020-05597-4CrossRef

27.

T. Tu, J. Zhou, Observer-based \(H_{\infty }\) control for uncertain one-sided lipschitz Markovian jump-delayed systems with partially unknown transition rates. Trans. Inst. Meas. Control. 45(11), 2192–2203 (2023). https://doi.org/10.1177/01423312221150030CrossRef

28.

G.L. Wang, Y.S. Ren, Stability analysis of Markovian jump systems with delayed impulses. Asian J. Control 25(2), 1047–1060 (2023). https://doi.org/10.1002/asjc.2863MathSciNetCrossRef

29.

G. Wang, Q. Zhang, Robust control of uncertain singular stochastic systems with Markovian switching via proportional-derivative state feedback. IET Control Theory Appl. 6(8), 1089–1096 (2012). https://doi.org/10.1049/iet-cta.2011.0549MathSciNetCrossRef

30.

J.R. Wang, H.J. Wang, A.K. Xue, R.Q. Lu, Delay-dependent \(H_{\infty }\) control for singular Markovian jump systems with time delay. Nonlinear Anal. Hybrid Syst. 8(1), 1–12 (2013). https://doi.org/10.1016/j.nahs.2012.08.003MathSciNetCrossRef

31.

Z.D. Wang, Y.R. Liu, X.H. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans. Autom. Control 55(7), 1656–1662 (2010). https://doi.org/10.1109/TAC.2010.2046114MathSciNetCrossRef

32.

Z.G. Wu, H.Y. Su, J. Chu, Delay-dependent \(H_{\infty }\) control for singular Markovian jump systems with time delay. Optim. Control Appl. Met. 30(5), 443–461 (2009). https://doi.org/10.1002/oca.860MathSciNetCrossRef

33.

J. Xie, Y.G. Kao, C.H. Zhang, H.R. Karimi, Quantized control for uncertain singular Markovian jump linear systems with general incomplete transition rates. Int. J. Control Autom. Syst. 15(3), 1107–1116 (2017). https://doi.org/10.1007/s12555-014-0171-8CrossRef

34.

S. Xu, J. Lam, Robust Control and Filtering of Singular Systems (Springer, Berlin, 2006)

35.

S.F. Yang, Y.N. Pan, L. Cao, L. Chen, Predefined-time fault-tolerant consensus tracking control for Multi-UAV systems with prescribed performance and attitude constraints. IEEE Trans. Aerospace Electr. Syst. (2024). https://doi.org/10.1109/TAES.2024.3371406CrossRef

36.

L.H. Zhang, Y.Y. Zhou, W.H. Qi, Non-fragile observer-based \(H_{\infty }\) finite-time sliding mode control. Appl. Math. Comput. 375, 125069 (2020). https://doi.org/10.1016/j.amc.2020.125069MathSciNetCrossRef

37.

Y.Q. Zhang, Y. Shi, P. Shi, Robust and non-fragile finite-time \(H_{\infty }\) control for uncertain Markovian jump nonlinear systems. Appl. Math. Comput. 279, 125–138 (2016). https://doi.org/10.1016/j.amc.2016.01.012MathSciNetCrossRef

38.

W.Y. Zhao, Y.C. Ma, A.H. Chen, L. Fu, Y.T. Zhang, Robust sliding mode control for Markovian jump singular systems with randomly changing structure. Appl. Math. Comput. 349, 81–96 (2019). https://doi.org/10.1016/j.amc.2018.12.014MathSciNetCrossRef

39.

X.D. Zhao, Q.S. Zeng, Delay-dependent Stability Analysis for Markovian Jump Systems with Interval Time-varying-delays. Int. J. Autom. Comput. 7(2), 224–229 (2010). https://doi.org/10.1007/s11633-010-0224-2MathSciNetCrossRef

40.

Y.Y. Zhou, G. Chen, Non-fragile \(H_{\infty }\) finite-time sliding mode control for stochastic Markovian jump systems with time delay. Appl. Math. Comput. 409, 126383 (2021). https://doi.org/10.1016/j.amc.2021.126383MathSciNetCrossRef

Title: Finite-Time Control for Time-Delayed Markovian Jump Nonlinear Systems with Parameter Uncertainties and Generally Uncertain Transition Rates
Authors: Chenyang Jiao
Juan Zhou
Publication date: 08-07-2024
Publisher: Springer US
Published in: Circuits, Systems, and Signal Processing / Issue 10/2024
Print ISSN: 0278-081X
Electronic ISSN: 1531-5878
DOI: https://doi.org/10.1007/s00034-024-02782-3

Springer Professional

Finite-Time \(H_\infty \) Control for Time-Delayed Markovian Jump Nonlinear Systems with Parameter Uncertainties and Generally Uncertain Transition Rates

Abstract

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

ATZelektronik

ATZelectronics worldwide

Springer Professional "Technik"

Other articles of this Issue 10/2024

Master–Slave Synchronization of Switched Nonlinear Systems Based on Quantization and Switching Event-Triggered Strategy

Fast Finite-Time Output Bipartite Tracking of Networked Heterogeneous Robotic Systems with Matrix-Weighted Digraphs

Blind Source Separation of Electromagnetic Signals Based on Swish-Tasnet

Optimized Adaptive Filter for Powerline Interference Cancellation in Electrocardiogram Signal Using a Modified Lightning Search Algorithm

A Novel Indirect Approach for Modelling a Class of Fractional-Order System in Complex Domain

Robust Equalizer Based on New Lower-Order Statistic Under Impulsive Noise Cases

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

ATZelektronik

ATZelectronics worldwide

Springer Professional "Technik"

Master–Slave Synchronization of Switched Nonlinear Systems Based on Quantization and Switching Event-Triggered Strategy

Fast Finite-Time Output Bipartite Tracking of Networked Heterogeneous Robotic Systems with Matrix-Weighted Digraphs

Blind Source Separation of Electromagnetic Signals Based on Swish-Tasnet

Optimized Adaptive Filter for Powerline Interference Cancellation in Electrocardiogram Signal Using a Modified Lightning Search Algorithm

A Novel Indirect Approach for Modelling a Class of Fractional-Order System in Complex Domain

Robust Equalizer Based on New Lower-Order Statistic Under Impulsive Noise Cases