A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

doi:10.1007/s10473-024-0320-y

Abstract

Abstract: Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system (HNSDDS) under a highly nonlinear constraint %high nonlinearity, in the $H_{\infty}$ and exponential forms. Nevertheless, the existing work just adapted to autonomous cases, and the obtained results were mainly on exponential stabilization. In comparison with autonomous cases, non-autonomous systems are of great interest and represent an important challenge. Accordingly, discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS, in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted. It should be noted, in particular, that the stabilization can be achieved not only in the routine $H_{\infty}$ and exponential forms, but also the polynomial form and even a general form.

Key words: hybrid neutral stochastic differential delay system, discrete feedback control, general stabilization, polynomial stabilization

CLC Number:

93D15

Lichao Feng, Chunyan Zhang, Jinde Cao, Zhihui Wu. A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY[J].Acta mathematica scientia,Series B, 2024, 44(3): 1145-1164.

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References

[1] Karimi H R.Robust delay-dependent $ H_ {\infty} $ control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and Markovian switching parameters. IEEE Transactions on Circuits and Systems I: Regular Papers, 2011, 58(8): 1910-1923
[2] Lee T H, Lakshmanan S, Park J H, et al. State estimation for genetic regulatory networks with mode-dependent leakage delays, time-varying delays,Markovian jumping parameters. IEEE Transactions on Nanobioscience, 2013, 12(4): 363-375
[3] Revathi V M, Balasubramaniam P, Park J H, et al. $H_{\infty}$ filtering for sample data systems with stochastic sampling and Markovian jumping parameters. Nonlinear Dynamics, 2014, 78(2): 813-830
[4] Feng L, Cao J, Liu L. Stability analysis in a class of Markov switched stochastic Hopfield neural networks. Neural Processing Letters, 2019, 50(1): 413-430
[5] Choi J, Lim C C. A Cholesky factorization based approach for blind FIR channel identification. IEEE Transactions on Signal Processing, 2008, 56(4): 1730-1735
[6] Boukas E K.Stochastic Switching Systems: Analysis and Design. Boston: Birkhauser, 2006
[7] Kolmanovskii V, Koroleva N, Maizenberg T, et al. Neutral stochastic differential delay equations with Markovian switching. Stochastic Analysis and Applications, 2003, 21(4): 819-847
[8] Xu S, Chu Y, Lu J, et al. Exponential dynamic output feedback controller design for stochastic neutral systems with distributed delays. IEEE Transactions on Systems, Man,Cybernetics-Part A: Systems and Humans, 2006, 36(3): 540-548
[9] Mao X, Shen Y, Yuan C. Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching. Stochastic Processes and Their Applications, 2008, 118(8): 1385-1406
[10] Bao J, Hou Z, Yuan C. Stability in distribution of neutral stochastic differential delay equations with Markovian switching. Statistics & Probability Letters, 2009, 79(15): 1663-1673
[11] Chen W, Zheng W, Shen Y. Delay-dependent stochastic stability and $H_{\infty}$-control of uncertain neutral stochastic systems with time delay. IEEE Transactions on Automatic Control, 2009, 54(7): 1660-1667
[12] Wu F, Hu S, Huang C. Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay. Systems & Control Letters, 2010, 59(3/4): 195-202
[13] Chen Y, Zheng W, Xue A.A new result on stability analysis for stochastic neutral systems. Automatica, 2010, 46(12): 2100-2104
[14] Zhu Q, Cao J. Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. Neurocomputing, 2010, 73: 2671-2680
[15] Pavlovic G, Jankovic S.The Razumikhin approach on general decay stability for neutral stochastic functional differential equations. Journal of the Franklin Institute, 2013, 350(8): 2124-2145
[16] Zhou W, Zhu Q, Shi P, et al. Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters. IEEE Transactions on Cybernetics, 2014, 44(12): 2848-2860
[17] Chen H, Shi P, Lim C C, et al. Exponential stability for neutral stochastic Markov systems with time-varying delay and its applications. IEEE Transactions on Cybernetics, 2015, 46(6): 1350-1362
[18] Obradović M, Milošević M. Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler-Maruyama method. Journal of Computational and Applied Mathematics, 2017, 309: 244-266
[19] Chen H, Yuan C. On the asymptotic behavior for neutral stochastic differential delay equations. IEEE Transactions on Automatic Control, 2018, 64(4): 1671-1678
[20] Li M, Deng F. Almost sure stability with general decay rate of neutral stochastic delayed hybrid systems with lévy noise. Nonlinear Analysis: Hybrid Systems, 2017, 24: 171-185
[21] Shen M, Fei W, Mao X, et al. Stability of highly nonlinear neutral stochastic differential delay equations. Systems & Control Letters, 2018, 115: 1-8
[22] Feng L, Wu Z, Cao J, et al. Exponential stability for nonlinear hybrid stochastic systems with time varying delays of neutral type. Applied Mathematics Letters, 2020, 107: 106468
[23] Feng L, Liu L, Cao J, et al. General decay stability for non-autonomous neutral stochastic systems with time-varying delays and Markovian switching. IEEE Transactions on Cybernetics, 2022, 52(6): 5441-5453
[24] Zhao Y, Zhu Q. Stability of highly nonlinear neutral stochastic delay systems with non-random switching signals. Systems & Control Letters, 2022, 165: 105261
[25] Hu L, Mao X. Almost sure exponential stabilisation of stochastic systems by state-feedback control. Automatica, 2008, 44: 465-471
[26] Ji Y, Chizeck H J. Controllability, stabilizability and continuous-time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control, 1990, 35: 777-788
[27] Mao X, Yin G, Yuan C. Stabilization and destabilization of hybrid systems of stochastic differential equations. Automatica, 2007, 43: 264-273
[28] Wu L, Su X, Shi P.Sliding mode control with bounded $L_{2}$ gain performance of Markovian jump singular time-delay systems. Automatica, 2012, 48(8): 1929-1933
[29] Mao X. Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control. Automatica, 2013, 49(12): 3677-3681
[30] Mao X, Liu W, Hu L, et al. Stabilization of hybrid stochastic differential equations by feedback control based on discretetime state observations. Systems & Control Letters, 2014, 73: 88-95
[31] You S, Liu W, Lu J, et al. Stabilization of hybrid systems by feedback control based on discrete-time state observations. SIAM Journal on Control and Optimization, 2015, 53(2): 905-925
[32] Song G, Zheng B, Luo Q, et al. Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode. IET Control Theory & Applications, 2017, 11(3): 301-307
[33] Lewis A L.Option Valuation Under Stochastic Volatility: With Mathematica Code. Newport Beach: Finance Press, 2000
[34] Luo Q, Mao X. Stochastic population dynamics under regime switching. Journal of Mathematical Analysis and Applications, 2007, 334: 69-84
[35] Zhu Y, Wang K, Ren Y. Dynamics of a mean-reverting stochastic volatility equation with regime switching. Communications in Nonlinear Science and Numerical Simulation, 2020, 83: 105110
[36] Fei C, Fei W, Mao X, et al. Stabilization of highly nonlinear hybrid systems by feedback control based on discrete-time state observations. IEEE Transactions on Automatic Control, 2020, 65(7): 2899-2912
[37] Feng L, Liu Q, Cao J, et al. Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems. Applied Mathematics and Computation, 2022, 417: 126771
[38] Mei C, Fei C, Shen M, et al. Discrete feedback control for highly nonlinear neutral stochastic delay differential equations with Markovian switching. Information Sciences, 2022, 592: 123-136
[39] Zhao Y, Zhu Q. Stabilization of stochastic highly nonlinear delay systems with neutral term. IEEE Transactions on Automatic Control, 2023, 68(4): 2544-2551
[40] Zhu Q. Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Transactions on Automatic Control, 2019, 64(9): 3764-3771
[41] Zhao Y, Zhu Q. Stabilization by delay feedback control for highly nonlinear switched stochastic systems with time delays. International Journal of Robust & Nonlinear Control, 2021, 31(8): 3070-3089
[42] Feng L, Liu L, Cao J, et al. General stabilization of non-autonomous hybrid systems with delays and random noises via delayed feedback control. Communications in Nonlinear Science and Numerical Simulation, 2023, 117: 106939
[43] Feng L, Li S, Song R, et al. Suppression of explosion by polynomial noise for nonlinear differential systems. Science China Information Sciences, 2018, 61(7): Art 70215