Stability of Highly Nonlinear Stochastic Delay Systems with Hybrid Switchings

• Yichi Liu ^[1] ; Quanxin Zhu ^[1]
  1. [1] Hunan Normal University

     Hunan Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01131-8
• Enlaces
  • Texto completo
• Resumen

  • Numerous studies have investigated the stability of highly nonlinear stochastic systems (HNSSs). However, previous works have primarily focused on either deterministic or random switchings. In this paper, we examine HNSSs with delays and two switching modes. First, we introduce a hybrid switching rule and construct a stopping time in segments, dividing the switching interval of the entire system into a deterministic switching interval and a stochastic switching interval. Second, we establish the existence and boundedness of the global solution of the system by using the Lyapunov function and the average dwell time method. Additionally, we prove the asymptotic stability and exponential stability of the system without relying on the linear growth condition (LGC). Finally, we provide an illustrative example to demonstrate the validity of the obtained results.

• Referencias bibliográficas
  • 1. Shen, M.X., Fei, W.Y., Mao, X.R., Liang, Y.: Stability of highly nonlinear neutral stochastic differential delay equations. Syst. Control...
  • 2. Song, R.L., Zhao, J.Y., Zhu, Q.X.: Boundedness and stability of nonlinear hybrid neutral stochastic delay differential equation with Levy...
  • 3. Fei, C., Fei, W.Y., Mao, X.R., Yan, L.T.: Delay-dependent asymptotic stability of highly nonlinear stochastic differential delay equations...
  • 4. Hu, J.H., Mao, W., Mao, X.R.: Advances in nonlinear hybrid stochastic differential delay equations: existence, boundedness and stability....
  • 5. Mao, X.R., Yuan, C.G., Zou, J.Z.: Stochastic differential delay equations of population dynamics. J. Math. Anal. Appl. 304(1), 296–320...
  • 6. Mackey, M.C., Nechaeva, I.G.: Solution moment stability in stochastic differential delay equations. Phys. Rev. 52(4), 3366 (1995)
  • 7. Mao, X.R., Sabanis, S.: Numerical solutions of stochastic differential delay equations under local Lipschitz condition. J. Comput. Appl....
  • 8. Li, H.T., Wang, Y.Z.: Controllability analysis and control design for switched Boolean networks with state and input constraints. SIAM...
  • 9. Liu, C.Y., Ryan, L., Lin, Q., Lay, T.: Kok: Dynamic optimization for switched time-delay systems with state-dependent switching conditions....
  • 10. Yuan, C., Wu, F.: Hybrid control for switched linear systems with average dwell time. IEEE Trans. Autom. Control 60, 240–245 (2015)
  • 11. Xu, N., Niu, B., Wang, H., Huo, X., Zhao, X.: Single-network ADP for solving optimal event-triggered tracking control problem of completely...
  • 12. Allerhand, L.I., Shaked, U.: Robust state-dependent switching of linear systems with dwell time. IEEE Trans. Autom. Control 58(4), 994–1001...
  • 13. Lin, H., Antsaklis, Panos J.: Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans. Autom....
  • 14. Chen, H.B., Shi, P., Lim, C.: Chew: Stability of neutral stochastic switched time delay systems: An average dwell time approach. Int....
  • 15. Zhao, Y., Zhu, Q.X.: Stability of highly nonlinear neutral stochastic delay systems with non-random switching signals. Syst. Control Lett....
  • 16. Mao, X.R.: Stability of stochastic differential equations with Markovian switchings. Stoch. Process. Appl. 79(1), 45–67 (1999)
  • 17. Mao, X.R., Matasov, A., Piunovskiy, A.B.: Stochastic differential delay equations with Markovian switching. Bernoulli 6(1), 73–90 (2000)
  • 18. Lee, J.W., Khargonekar, P.P.: Optimal output regulation for discrete-time switched and Markovian jump linear systems. SIAM J. Control....
  • 19. Li, W.R., Fei, C., Shen, M.X., Fei, W.Y., Mao, X.R.: A stabilization analysis for highly nonlinear neutral stochastic delay hybrid systems...
  • 20. Xiang, W.M., Lam, J., Li, P.S.: On stability and H∞ control of switched systems with random switching signals. Automatica 95, 419–425...
  • 21. Xiong, J.L., Mao, X.R., Shu, Z.: Stability analysis of continuous-time switched systems with a random switching signal. IEEE Trans. Autom....
  • 22. Chatterjee, D., Liberzon, D.: On stability of randomly switched nonlinear systems. IEEE Trans. Autom. Control 52(12), 2390–2394 (2007)
  • 23. Zhu, F.B., Han, Z.Z., Zhang, J.F.: Stability analysis of atochastic differential equations with Markovian switching. Syst. Control Lett....
  • 24. Shi, P., Shi, Y., Zong, G.D., Yang, D.: Adaptive tracking control of hybrid switching Markovian systems with its applications. SIAM J....
  • 25. Hespanha, J.P., Morse, A. S.: Stability of switched systems with average dwell-time. Proceedings of the 38th IEEE Conference on Decision...
  • 26. Wang, B., Zhu, Q.X.: Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems....
  • 27. Shen, M.X., Fei, C., Fei, W.Y.: Stabilisation by delay feedback control for highly nonlinear neutral stochastic differential equations....
  • 28. Shen, M.X., Fei, W.Y., Mao, X.R., Deng, S.N.: Exponential stability of highly nonlinear neutral pantograph stochastic differential equations....
  • 29. Mao, X.R.: Stochastic differential equations and applications. Horwood Publishing Limited, Chichester (2007)
  • 30. Shi, S., Fei, Z.Y., Li, J.C.: Finite-time H∞ control of switched systems with mode-dependent average dwell time. J. Franklin Inst. 353,...