Adaptive state feedback stabilisation for more general switched stochastic non-linear systems under arbitrary switchings

In this study, the problem of adaptive state feedback stabilisation of switched stochastic non-linear systems is addressed. To overcome the uncertainty of arbitrary switchings, a novel common Lyapunov function is constructed in the authors' control scheme. By integrating adaptive control technique and homogeneity with monotone degrees into backstepping framework, a common state feedback control law independent of switching signal is designed recursively under weaker non-linear growth conditions. A distinct feature of non-linear conditions is that the parameters $\tau _i$tau i ($i=1,2,\ldots ,n$i=1,2, horizontal ellipsis ,n) can be chosen as different values rather than a unified value in the existing literature. Finally, a simulation example is presented to show the effectiveness of their control scheme.