Taking different structures in different modes into account, the paper has developed a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations (SDDEs) without the linear growth condition. A new Lyapunov function is designed in order to deal with the effects of different structures as well as those of different parameters within the same modes. Moreover, a lot of effort is put into showing the almost sure asymptotic stability in the absence of the linear growth condition.
Fei, W., Hu, L., Mao, X., & Shen, M. (2018). Structured robust stability and boundedness of nonlinear hybrid delay systems. SIAM Journal on Control and Optimization, 56(4), 2662–2689. https://doi.org/10.1137/17M1146981