Publication Cover
Automatika
Journal for Control, Measurement, Electronics, Computing and Communications
Volume 64, 2023 - Issue 4
378
Views
0
CrossRef citations to date
0
Altmetric
Regular Papers

Almost sure stability of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals

, , &
Pages 1296-1305 | Received 21 May 2022, Accepted 18 Sep 2023, Published online: 06 Oct 2023

References

  • Gong WL, Xiao J, Han S, et al. Research on robot wireless charging system based on constant-voltage and constant-current mode switching. Energy Rep. 2022;8(4):940–948. doi:10.1016/j.egyr.2022.02.025
  • Zhang XL, Huang Y, Wang ST, et al. Hierarchical autonomous switching control of a multi-modes omnidirectional mobile robot. Mechatronics. 2021;80:102692. doi:10.1016/j.mechatronics.2021.102692
  • Qu L, Yu ZQ, Zeng R, et al. Parallel breaking characteristics of diode-bridge power electronic switch for DC circuit breaker. Int J Electr Power Energy Syst. 2022;138:107929. doi:10.1016/j.ijepes.2021.107929
  • Himanshukumar RP, Vipul AS. A metaheuristic approach for interval type-2 fuzzy fractional order fault-tolerant controller for a class of uncertain nonlinear system. Automatika. 2022;63(4):656–675. doi:10.1080/00051144.2022.2061818
  • Himanshukumar RP, Vipul AS. Type-2 fuzzy logic applications designed for active parameter adaptation in metaheuristic algorithm for fuzzy fault-tolerant controller. Int J Intell Comput Cybern. 2023;16(2):198–222. doi:10.1108/IJICC-01-2022-0011
  • Himanshukumar RP. Fuzzy-based metaheuristic algorithm for optimization of fuzzy controller: fault-tolerant control application. Int J Intell Comput Cybern. 2022;15(4):599–624. doi:10.1108/IJICC-09-2021-0204
  • Raval S, Himanshukumar RP, Vipul AS. Neural network-based control framework for SISO uncertain system: passive fault tolerant approach. INFUS 2020: Intelligent and Fuzzy Techniques: Smart and Innovative Solutions, AISC 1197; 2021. p. 1039–1047.
  • Himanshukumar RP, Vipul AS. Stable fault tolerant controller design for Takagi-Sugeno fuzzy model-based control systems via linear matrix inequalities: three conical tank case study. Energies. 2019;12:2221. doi:10.3390/en12112221
  • Himanshukumar RP, Vipul AS. Shadowed Type-2 fuzzy sets in dynamic parameter adaption in cuckoo search and flower pollination algorithms for optimal design of fuzzy fault-tolerant controllers. Math Comput Appl. 2022;27:89.
  • Raval S, Himanshukumar RP, Vipul AS. Fault tolerant controller comparative study and analysis for benchmark two tank interacting level control system. SN Computer Science. 2021;2:93. doi:10.1007/s42979-021-00489-9
  • Himanshukumar RP, Vipul AS. Stable fuzzy controllers via LMI approach for non-linear systems described by type-2 T–S fuzzy model. Int J Intell Comput Cybern. 2021;14(3):509–531. doi:10.1108/IJICC-02-2021-0024
  • Himanshukumar RP, Raval SK, Vipul AS. A novel design of optimal intelligent fuzzy TID controller employing GA for nonlinear level control problem subject to actuator and system component fault. Int J Intell Comput Cybern. 2021;14(1):17–32. doi:10.1108/IJICC-11-2020-0174
  • Himanshukumar RP, Vipul AS. A fractional and integer order PID controller for nonlinear system: two non-interacting conical tank process case study. Advances in control systems and its infrastructure. Lect Notes Electr Eng. 2020;604:37–55. doi:10.1007/978-981-15-0226-2_4
  • Zhao XD, Yin YF, Zheng XL. State-dependent switching control of switched positive fractional-order systems. ISA Trans. 2016;62:103–108. doi:10.1016/j.isatra.2016.01.011
  • Zhan T, Ma S, Li W, et al. Exponential stability of fractional-order switched systems with mode-dependent impulses and its application. IEEE Trans Cybern. 2022;52(11):11516–11525.
  • Yang Y, Chen G. Stability of a class of fractional order switched systems, IEEE Advanced Information Technology. Electronic and Automation Control Conference (IAEAC); 2015. p. 87–90.
  • Sakthivel R, Mohanapriya S, Ahn CK, et al. Output tracking control for fractional-order positive switched systems with input time delay. IEEE Trans Circuits Syst Express Briefs. 2019;66(6):1013–1017. doi:10.1109/TCSII.2018.2871034
  • Zhang XF, Wang Z. Stability and robust stabilization of uncertain switched fractional order systems. ISA Trans. 2020;103:1–9. doi:10.1016/j.isatra.2020.03.019
  • Feng T, Guo LH, Wu BW, et al. Stability analysis of switched fractional-order continuous-time systems. Nonlinear Dyn. 2020;102:2467–2478. doi:10.1007/s11071-020-06074-8
  • Mai VT, Dinh CH. Robust finite-time stability and stabilization of a class of fractional-order switched nonlinear systems. J Syst Sci Complex. 2019;32:1479–1497. doi:10.1007/s11424-019-7394-y
  • Feng T, Wu B, Liu L, et al. Finite-time stability and stabilization of fractional-order switched singular continuous-time systems. Circuits Syst Signal Process. 2019;38:5528–5548. doi:10.1007/s00034-019-01159-1
  • Liang J, Wu B, Wang Y, et al. Input–output finite-time stability of fractional-order positive switched systems. Circuits Syst Signal Process. 2019;38:1619–1638. doi:10.1007/s00034-018-0942-1
  • Zhang J, Zhao X, Chen Y. Finite-time stability and stabilization of fractional order positive switched systems. Circuits Syst Signal Process. 2016;35:2450–2470. doi:10.1007/s00034-015-0236-9
  • Liu L, Cao X, Fu Z, et al. Finite-time control of uncertain fractional-order positive impulsive switched systems with mode-dependent average dwell time. Circuits Syst Signal Process. 2018;37:3739–3755. doi:10.1007/s00034-018-0752-5
  • Arwade S, Lackner M, Grigoriu M. Probabilistic models for wind turbine and wind farm performance. J Solar Energy Eng. 2011;133:041006. doi:10.1115/1.4004273
  • Palejiya D, Hall J, Mecklenborg C, et al. Stability of wind turbine switching control in an integrated wind turbine and rechargeable battery system: a common quadratic Lyapunov function approach, J Dyn Syst Meas Control. 2013;135:021018.
  • Song Y, Yang J, Yang T, et al. Almost sure stability of switching Markov jump linear systems. IEEE Trans Autom Control. 2016;61:2638–2643. doi:10.1109/TAC.2015.2505405
  • Long F, Liu C, Ou W. Almost sure stability for a class of dual switching linear discrete-time systems. Concurr Comput Pr Exper. 2021;33(15):e5666). doi:10.1002/cpe.5666
  • Liu L, Long F, Mo L, et al. Sign stability of dual switching linear continuous-time positive systems. Symmetry. 2021;13:2194. doi:10.3390/sym13112194
  • Bolzern P, Colaneri P, De Nicolao G. Almost sure stability of Markov jump linear systems with deterministic switching. IEEE Trans Autom Control. 2013;58:209–214. doi:10.1109/TAC.2012.2203049
  • Colaneri P. Dwell time analysis of deterministic and stochastic switched systems. Eur J Control. 2009;15:228–248. doi:10.3166/ejc.15.228-248
  • Bolzern P, Colaneri P, De Nicolao G. Markov jump linear systems with switching transition rates: mean square stability with dwell-time. Automatica. 2010;46:1081–1088. doi:10.1016/j.automatica.2010.03.007
  • Wu C, Liu X. Lyapunov and external stability of Caputo fractional order switching systems. Nonlinear Anal Hybrid Syst. 2019;34:131–146. doi:10.1016/j.nahs.2019.06.002
  • Liang J, Wu B, Wang Y, et al. Input-output finite-time stability of fractional-order positive switched systems. Circuits Syst Signal Process. 2019;38:1619–1638. doi:10.1007/s00034-018-0942-1
  • Hu J. Comments on “Lyapunov and external stability of Caputo fractional order switching systems”. Nonlinear Anal: Hybrid Syst. 2021;40:101016. doi:10.1016/j.nahs.2021.101016
  • Hu J. Comments on “input-output finite-time stability of fractional-order positive switched systems. Circuits Syst Signal Process. 2021;40:510–514. doi:10.1007/s00034-020-01485-9
  • Wu C, Liu X. Updating is significant to Caputo fractional order switching systems: a reply to hus comments. Nonlinear Anal Hybrid Syst. 2022;44:101123. doi:10.1016/j.nahs.2021.101123
  • Norris J. Markov chains. New York: Cambridge University Press; 2009.
  • Wu X, Tang Y, Cao J, et al. Stability analysis for continuous-time switched systems with stochastic switching signals. IEEE Trans Autom Control. 2018;63:3083–3090. doi:10.1109/TAC.2017.2779882
  • Chatterjee D, Liberzon D. On stability of randomly switched nonlinear systems. IEEE Trans Autom Control. 2007;52:2390–2394. doi:10.1109/TAC.2007.904253
  • Butzer P, Westphal U. An introduction to fractional calculus, World Scientific. Singapore; 2000.
  • Ye H, Gao J, Ding Y. A generalized Gronwall-Bellman inequality and its application to a fractional differential equation. J Math Anal Appl. 2007;328:1075–1081. doi:10.1016/j.jmaa.2006.05.061
  • Bolzern P, Colaneri P, Nicolao GD. Design of stabilizing strategies for dual switching stochastic-deterministic linear systems. Proceedings of the 19th World Congress, the International Federation of Automatic Control Cape Town, South Africa. August, 2014, 24–29.