The novel impulsive switching conditions for stability of impulsive switched stochastic systems

References

• Ai, Z., & Zong, G. (2014). Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems. Applied Mathematics and Computation, 245, 462–473. https://doi.org/10.1016/j.amc.2014.07.092
   Web of Science ®Google Scholar
• Branicky, M. (1998). Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 43(4), 475–482. https://doi.org/10.1109/9.664150
   Web of Science ®Google Scholar
• Buyukkoroglu, T., Esen, O., & Dzhafarov, V. (2011). Common Lyapunov Functions for Some Special Classes of Stable Systems. IEEE Transactions on Automatic Control, 56(8), 1963–1967. https://doi.org/10.1109/TAC.2011.2137510
   Web of Science ®Google Scholar
• Daafouz, J., Riedinger, P., & Iung, C. (2002). Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Transactions on Automatic Control, 47(11), 1883–1887. https://doi.org/10.1109/TAC.2002.804474
   Web of Science ®Google Scholar
• Dashkovskiy, S., & Mironchenko, A. (2013). Input-to-State stability of nonlinear impulsive systems. SIAM Journal on Control and Optimization, 51(3), 1962–1987. https://doi.org/10.1137/120881993
   Web of Science ®Google Scholar
• Dayawansa, W. P., & Martin, C. F. (1999). A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Transactions on Automatic Control, 44(4), 751–760. https://doi.org/10.1109/9.754812
   Web of Science ®Google Scholar
• Decarlo, R., Branicky, M., Pettersson, S., & Lennartson, B. (2000). Perspectives and results on the stability and stabilizability of hybrid systems. Proceedings of the IEEE, 88(7), 1069–1082. https://doi.org/10.1109/5.871309
   Web of Science ®Google Scholar
• Haltar, D., & Ankhbayar, G. (2008). Using the maximum principle of impulse control for ecology-economical models. Ecological Modelling, 216(2), 150–156. https://doi.org/10.1016/j.ecolmodel.2008.03.025
   Web of Science ®Google Scholar
• He, X., Li, X., & Song, S. (2022). Finite-time input-to-state stability of nonlinear impulsive systems. Automatica, 135, 109994. https://doi.org/10.1016/j.automatica.2021.109994
   Web of Science ®Google Scholar
• Hespanha, J. (2004). Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle. IEEE Transactions on Automatic Control, 49(4), 470–482. https://doi.org/10.1109/TAC.2004.825641
   Web of Science ®Google Scholar
• Hespanha, J. P., Liberzon, D., & Teel, A. R. (2008). Lyapunov conditions for input-to-state stability of impulsive systems. Automatica, 44(11), 2735–2744. https://doi.org/10.1016/j.automatica.2008.03.021
   Web of Science ®Google Scholar
• Kundu, A., Chatterjee, D., & Liberzon, D. (2016). Generalized switching signals for input-to-state stability of switched systems. Automatica, 64, 270–277. https://doi.org/10.1016/j.automatica.2015.11.027
   Web of Science ®Google Scholar
• Li, X., Bohner, M., & Wang, C. K. (2015). Impulsive differential equations: Periodic solutions and applications. Automatica, 52, 173–178. https://doi.org/10.1016/j.automatica.2014.11.009
   Web of Science ®Google Scholar
• Liberzon, D. (2003). Switching in systems and control. Birkhauser.
   Google Scholar
• Lin, H., & Antsaklis, P. J. (2009). Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Transactions on Automatic Control, 54(2), 308–322. https://doi.org/10.1109/TAC.2008.2012009
   Web of Science ®Google Scholar
• Liu, J., Liu, X., & Xie, W. C. (2009). Uniform stability of switched nonlinear systems. Nonlinear Analysis: Hybrid Systems, 3(4), 441–454. https://doi.org/10.1016/j.nahs.2009.03.001
   Web of Science ®Google Scholar
• Mancilla-Aguilar, J., & Garcia, R. (2001). On converse Lyapunov theorems for ISS and iISS switched nonlinear systems. Systems & Control Letters, 42(1), 47–53. https://doi.org/10.1016/S0167-6911(00)00079-7
   Web of Science ®Google Scholar
• Ren, W., & Xiong, J. (2017). Stability analysis of impulsive stochastic nonlinear systems. IEEE Transactions on Automatic Control, 62(9), 4791–4797. https://doi.org/10.1109/TAC.2017.2688350
   Web of Science ®Google Scholar
• Revuz, D., & Yor, M. (1999). Continuous martingales and Brownian motion. Springer-Verlag.
   Google Scholar
• Sontag, E. (1989). Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control, 34(4), 435–443. https://doi.org/10.1109/9.28018
   Web of Science ®Google Scholar
• Van Schuppen, J. (1992). Jump linear systems in automatic control: M Mariton. Automatica, 28(6), 1284–1285. https://doi.org/10.1016/0005-1098(92)90075-Q
   Google Scholar
• Wang, P., Wang, X., & Su, H. (2021). Input-to-state stability of impulsive stochastic infinite dimensional systems with poisson jumps. Automatica, 128, 109553. https://doi.org/10.1016/j.automatica.2021.109553
   Web of Science ®Google Scholar
• Wu, H., & Sun, J. (2006). p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching. Automatica, 42(10), 1753–1759. https://doi.org/10.1016/j.automatica.2006.05.009
   Web of Science ®Google Scholar
• Xu, H., & Teo, K. L. (2010). Exponential stability with L2-Gain condition of nonlinear impulsive switched systems. IEEE Transactions on Automatic Control, 55(10), 2429–2433. https://doi.org/10.1109/TAC.2010.2060173
   Web of Science ®Google Scholar
• Zhang, L., & Gao, H. (2010). Asynchronously switched control of switched linear systems with average dwell time. Automatica, 46(5), 953–958. https://doi.org/10.1016/j.automatica.2010.02.021
   Web of Science ®Google Scholar
• Zhang, L., & Shi, P. (2008). l2−l∞ model reduction for switched LPV systems with average dwell time. IEEE Transactions on Automatic Control, 53(10), 2443–2448. https://doi.org/10.1109/TAC.2008.2007860
   Web of Science ®Google Scholar
• Zhao, P., Feng, W., & Kang, Y. (2012). Stochastic input-to-state stability of switched stochastic nonlinear systems. Automatica, 48(10), 2569–2576. https://doi.org/10.1016/j.automatica.2012.06.058
   Web of Science ®Google Scholar
• Zhao, X., Shi, P., Yin, Y., & Nguang, S. K. (2017). New results on stability of slowly switched systems: A multiple discontinuous Lyapunov function approach. IEEE Transactions on Automatic Control, 62(7), 3502–3509. https://doi.org/10.1109/TAC.2016.2614911
   Web of Science ®Google Scholar
• Zhao, X., Zhang, L., Shi, P., & Liu, M. (2012). Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Transactions on Automatic Control, 57(7), 1809–1815. https://doi.org/10.1109/TAC.2011.2178629
   Web of Science ®Google Scholar