References
- Willsky AS, Levy BC. Stochastic stability research for complex power systems. DOE Contract, LIDS, MIT, Report ET-76-C-01-2295: 1979.
- Sworder D, Rogers R. An LQ-solution to a control problem associated with solar thermal central receiver. IEEE Trans Automat Control. 1983;28:971–978. doi: https://doi.org/10.1109/TAC.1983.1103151
- Mariton M. Jump linear systems in automatic control. New York (NY): Marcel Dekker; 1990.
- Ghosh MK, Arapostathis A, Marcus SI. Optimal control of switching diffusions with application to flexible manufacturing systems. SIAM J Control Optim. 1993;31(5):1183–1204. doi: https://doi.org/10.1137/0331056
- Yin G, Liu RH, Zhang Q. Recursive algorithms for stock liquidation: a stochastic optimization approach. SIAM J Optim. 2002;13(1):240–263. doi: https://doi.org/10.1137/S1052623401392901
- Mao X, Yuan C. Stochastic differential equations with Markovian switching. London: Imperial College Press; 2006.
- Yin GG, Zhu C. Hybrid switching diffusions: properties and applications. New York (NY): Springer; 2010.
- Rakkiyappan R, Chandrasekar A, Lakshmanan S, et al. Exponential stability of Markovian jumping stochastic Cohen–Grossberg neural networks with mode-dependent probabilistic time-varying delays and impulses. Neurocomputing. 2014;131:265–277. doi: https://doi.org/10.1016/j.neucom.2013.10.018
- Kushner H. Stochastic stability and control. New York (NY): Academic Press; 1976.
- Khasminskii RZ. Stochastic stability of differential equations. Leiden: Sijthoff and Noordhoff; 1981.
- Ji Y, Chizeck HJ. Controllability, stabilizability and continuous-time Markovian jump linear quadratic control. IEEE Trans Automat Contr. 1990;35:777–788. doi: https://doi.org/10.1109/9.57016
- Mao X, Yin G, Yuan C. Stabilization and destabilization of hybrid systems of stochastic differential equations. Automatica. 2007;43:264–273. doi: https://doi.org/10.1016/j.automatica.2006.09.006
- Wu L, Shi P, Gao H. State estimation and sliding mode control of Markovian jump singular systems. IEEE Trans Automat Contr. 2010;55(5):1213–1219. doi: https://doi.org/10.1109/TAC.2010.2042234
- Teel A, Subbaramana A, Sferlazza A. Stability analysis for stochastic hybrid systems: a survey. Automatica. 2014;50:2435–2456. doi: https://doi.org/10.1016/j.automatica.2014.08.006
- Chang L, Sun G, Wang Z, et al. Rich dynamics in a spatial predator-prey model with delay. Appl Math Comput. 2015;256:540–550.
- Mohammed SEA. Stochastic functional differential equations. Harlow: Longman Scientific and Technical; 1986.
- Shaikhet L. Stability of stochastic hereditary systems with Markov switching. Theory Stoch Processes. 1996;2(18):180–184.
- Kolmanovskii VB, Myshkis A. Introduction to the theory and applications of functional differential equations. Dordrecht: Kluwer Academic Publishers; 1999.
- Mao X, Matasov A, Piunovskiy AB. Stochastic differential delay equations with Markovian switching. Bernoulli. 2000;6(1):73–90. doi: https://doi.org/10.2307/3318634
- Mao X. Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans Automat Control. 2002;47(10):1604–1612. doi: https://doi.org/10.1109/TAC.2002.803529
- Yue D, Han Q. Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity and Markovian switching. IEEE Trans Automat Control. 2005;50:217–222. doi: https://doi.org/10.1109/TAC.2004.841935
- Wei G, Wang Z, Shu H, et al. Robust H∞ control of stochastic time-delay jumping systems with nonlinear disturbances. Optim Control Appl Meth. 2006;27:255–271. doi: https://doi.org/10.1002/oca.780
- Basin M, Rodkina A. On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays. Nonlinear Anal. 2008;68(8):2147–2157. doi: https://doi.org/10.1016/j.na.2007.01.046
- Wu L, Su X, Shi P. Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems. Automatica. 2012;48(8):1929–1933. doi: https://doi.org/10.1016/j.automatica.2012.05.064
- Hu L, Mao X, Shen Y. Stability and boundedness of nonlinear hybrid stochastic differential delay equations. Syst Control Lett. 2013;62:178–187. doi: https://doi.org/10.1016/j.sysconle.2012.11.009
- Wang G, Zhang Q, Yang C. Exponential stability of stochastic singular delay systems with general Markovian switchings. Int J Robust Nonlinear Control. 2015;25:3478–3494. doi: https://doi.org/10.1002/rnc.3276
- Mao X. Stability and stabilization of stochastic differential delay equations. IET Control Theory Appl. 2007;1(6):1551–1566. doi: https://doi.org/10.1049/iet-cta:20070006
- Li X, Zhu F, Chakrabarty A, et al. Non-fragile fault-tolerant fuzzy observer-based controller design for nonlinear systems. IEEE Trans Fuzzy Syst. 2016;24(6):1679–1689. doi: https://doi.org/10.1109/TFUZZ.2016.2540070
- Ge C, Wang H, Liu Y, et al. Further results on stabilization of neural-network-based systems using sampled-data control. Nonlinear Dyn. 2017;90:2209–2219. doi: https://doi.org/10.1007/s11071-017-3796-3
- Park C, Kwon NK, Park P. Output-feedback control for singular Markovian jump systems with input saturation. Nonlinear Dyn. 2018;93:1231–1240. doi: https://doi.org/10.1007/s11071-018-4255-5
- Wang Z, Qiao H, Burnham KJ. On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters. IEEE Trans Automat Control. 2002;47(4):640–646. doi: https://doi.org/10.1109/9.995042
- Mao X, Lam J, Huang L. Stabilization of hybrid stochastic differential equations by delay feedback control. Syst Control Lett. 2008;57:927–935. doi: https://doi.org/10.1016/j.sysconle.2008.05.002
- Deng F, Luo Q, Mao X. Stochastic stabilization of hybrid differential equations. Automatica. 2012;48:2321–2328. doi: https://doi.org/10.1016/j.automatica.2012.06.044
- Mao X. Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control. Automatica. 2013;49(12):3677–3681. doi: https://doi.org/10.1016/j.automatica.2013.09.005
- Mao X, Liu W, Hu L, et al. Stabilization of hybrid SDEs by feedback control based on discrete-time state observations. Syst Control Lett. 2014;73:88–95. doi: https://doi.org/10.1016/j.sysconle.2014.08.011
- You S, Liu W, Lu J, et al. Stabilization of hybrid systems by feedback control based on discrete-time state observations. SIAM J Control Optim. 2015;53(2):905–925. doi: https://doi.org/10.1137/140985779
- Yang J, Zhou W, Shi P, et al. Synchronization of delayed neural networks with L e´vy noise and Markovian switching via sampled data. Nonlinear Dyn. 2015;81(3):1179–1189. doi: https://doi.org/10.1007/s11071-015-2059-4
- Wu Y, Yan S, Fan M, et al. Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete-time state observations. Int J Robust Nonlinear Control. 2018;28:247–265. doi: https://doi.org/10.1002/rnc.3867
- Zhao Y, Zhang Y, Xu T, et al. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. Discrete Contin Dyn Syst Ser B. 2017;22(1):209–226.
- Li Y, Lu J, Kou C, et al. Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique. Stat Probab Lett. 2018;139:152–161. doi: https://doi.org/10.1016/j.spl.2018.02.058
- Geromel JC, Gabriel GW. Optimal H2 state feedback sampled-data control design of Markov jump linear system. Automatica. 2015;54:182–188. doi: https://doi.org/10.1016/j.automatica.2015.02.011
- Li Y, Lu J, Mao X, et al. Stabilization of hybrid systems by feedback control based on discrete-time state and mode observations. Asian J Control. 2017;19(6):1943-–1953. doi: https://doi.org/10.1002/asjc.1515
- Anderson WJ. Continuous-time Markov chains. New York (NY): Springer; 1991.
- Li X, Mao X. Stabilisation of highly nonlinear hybrid stochastic differential delay equations by delay feedback control. Automatica. 2020;112:108657.