This work is concerned with the finite-time input-to-state stability (FTISS) for impulsive switched stochastic time-delay systems. Two cased of hybrid systems are investigated: (i) the impulsive instants and switching instants are synchronous; (ii) the impulsive instants and switching instants are asynchronous. Furthermore, we allow the upper bound of Lyapunov-Razumikhin function with two indefinite derivatives. Then, by using the technique of Lyapunov-Razumikhin, comparison principles combined with the mode-dependent average dwell time (MDADT) and the mode-dependent average impulsive interval (MDAII), we obtain the FTISS property. Finally, we give an example to apply our result and verify its effectiveness.
GoebelRSanfeiceRGTeelAR.Hybrid dynamical systems: modeling, stability, and robustness. Princeton University Press, 2012.
2.
LavaeiAFrazzoliE.Scalable synthesis of safety barrier certificates for networks of stochastic switched systems. IEEE Trans Automat Contr2024; 69(11): 7294–7309.
3.
WuGSunJChenJ.Optimal linear quadratic regulator of switched systems. IEEE Trans Automat Contr2019; 64(7): 2898–2904.
4.
WuFLiXZhangX.Stochastic linear quadratic optimal control problems with regime-switching jumps in Infinite Horizon. SIAM J Control Optim2025; 63(2): 852–891.
5.
JiaoSXuSParkJH.Hybrid-triggered-based control against denial-of-Service attacks for fuzzy switched systems with persistent dwell-time. IEEE Trans Fuzzy Syst2024; 32(3): 710–720.
6.
ZhangWChenJWenS, et al. Event-triggered random delayed impulsive consensus of multi-agent systems with time-varying delay. IEEE Trans Emerg Top Comput Intell2025; 9: 2059–2064.
7.
SuHWuYZhengWX.Distributed observer for LTI systems under stochastic impulsive sequential attacks. Automatica2024; 159: 111370.
8.
LiuXChengPCuiY.Stabilization and destabilization of impulsive Markovian switching systems via periodic stochastic controls and impulsive controls. Int J Robust Nonlinear Control2024; 34(5): 3224–3240.
9.
XieYGaoLYangS.Input-to-state stability of impulsive switched systems under mode-dependent event-triggered impulsive control. Trans Inst Meas Contr2025; 47: 454–464.
10.
WangZGaoLLiuH.Stability and stabilization of impulsive switched system with inappropriate impulsive switching signals under asynchronous switching. Nonlinear Anal Hybrid Syst2021; 39: 100976.
11.
LiuSTanwaniA.Impulsive switching signals with functional inequalities: Stability analysis using hybrid systems framework. Automatica2025; 171: 111928.
12.
ZhangTLiXCaoJ.Finite-time stability of impulsive switched systems. IEEE Trans Automat Contr2023; 68(9): 5592–5599.
13.
ZhangTCaoJLiX.Lyapunov conditions for finite-time input-to-state stability of impulsive switched systems. IEEE CAA Journal of Automatica Sinica2024; 11(4): 1057–1059.
14.
PengHZhuQ.New criteria of stochastic finite time stability for impulsive switched stochastic nonlinear systems. Commun Nonlinear Sci Numer Simul2025; 142: 108545.
15.
WangZSunJChenJ.Input-to-state stability of impulsive switched nonlinear time-delay systems with two asynchronous switching phenomena. Int J Robust Nonlinear Control2020; 30: 4463–4484.
16.
ZhangJNieX.Exponential stability of fractional-order asynchronous switched impulsive systems with time delay and mode-dependent parameter uncertainty. J Franklin Inst2025; 362(1): 107406.
17.
YanZZhouXJiD, et al. Finite-time annular domain stability and stabilisation of Itô-type stochastic time-varying systems with Wiener and Poisson noises. Int J Control2023; 96: 374–391.
18.
WangZSunJChenJ, et al. Finite-time stability of switched nonlinear time-delay systems. Int J Robust Nonlinear Control2020; 30(7): 2906–2919.
19.
ZhangTCaoJAbdel-AtyM, et al. Finite-time stability of impulsive and switched hybrid systems with delay-dependent impulses. IEEE/CAA Journal of Automatica Sinica2025; 12(2): 466–468.
20.
ZhongSZhangW.Finite-time stability and stabilization for highly nonlinear stochastic Markov jump systems. ISA Trans2025; 160: 131–138.
SontagED.Comments on integral variants of ISS. Syst Control Lett1998; 34: 93–100.
23.
ZhangMZhuQ.New criteria of input-to-state stability for nonlinear switched stochastic delayed systems with asynchronous switching. Syst Control Lett2019; 129: 43–50.
24.
LiuQHeYNingC.Indefinite multiple Lyapunov functions ofpth moment input-to-state stability andpth moment integral input-to-state stability for the nonlinear time-varying stochastic systems with Markovian switching. Int J Robust Nonlinear Control2021; 31: 5343–5359. 2021.
25.
WuXTangYCaoJ.Input-to-state stability of time-varying switched systems with time delays. IEEE Trans Automat Contr2019; 64(6): 2537–2544.
26.
SanjeeviniSLaiBKoubaO, et al. Input-to-state stability of discrete-time, linear time-varying systems. Automatica2025; 177: 112331.
27.
HongYJiangZPFengG.Finite-time input-to-state stability and applications to finite-time control design. SIAM J Control Optim2010; 48(7): 4395–4418.
28.
HeXLiXSongS.Finite-time input-to-state stability of nonlinear impulsive systems. Automatica2022; 135: 109994.
29.
WangZCaoJCaiZ.Sufficient conditions on finite-time input-to-state stability of nonlinear impulsive systems: a relaxed Lyapunov function method. Int J Control2022; 95: 2992–3001. 2021.
30.
WangZSunJChenJ.Finite-time integral input-to-state stability for switched nonlinear time-delay systems with asynchronous switching. Int J Robust Nonlinear Control2021; 31(9): 3929–3954.
31.
ZhangMZhuQ.Finite-time input-to-state stability of switched stochastic time-varying nonlinear systems with time delays. Chaos Solitons Fractals2022; 162: 112391.
32.
ZhangMZhuQ.Sufficient conditions on finite-time input-to-state stability of nonlinear stochastic impulsive time-varying systems. Int J Robust Nonlinear Control2023; 33(11): 6417–6430.
33.
GargKPanagouD. Finite-time stability of switched and hybrid systems. DOI:10.48550/arXiv.1901.08513.
34.
ClarkeF.Optimization and nonsmooth analysis. Wiley-Press, 1983.
35.
MaoXR.Stochastic differential equations and applications. Howrwood, 2007.
36.
WangZChenGXiaJ.Finite-time input/output-to-state stability of impulsive switched nonlinear time-delay systems. IEEE Trans Circuits Syst II Express Briefs2022; 69(8): 3585–3589.
