Stochastic input/output-to-state stability of switched nonlinear systems with stable and unstable subsystems

In this paper, the notions of stochastic input/output-to-state stability (SIOSS) and pth moment IOSS are introduced to stochastic nonlinear systems. As an extension, we also consider the IOSS property of switched stochastic nonlinear systems under average dwell-time switching signals, both when all constituent subsystems are IOSS in probability (in pth moment) and when only some of them are IOSS in probability (in pth moment) while some others are not. Moreover, the conclusions in this paper are also applicable for the analysis of pth ISS/SISS for switched systems. As the results, the corresponding Lyapunov-type sufficient criteria of pth moment IOSS and SIOSS are given. Finally, a simulation example is given to demonstrate the effectiveness of the proposed results.