Adaptive state feedback control for switched stochastic high‐order nonlinear systems under arbitrary switchings

This paper studies the adaptive state feedback control for a class of switched time‐varying stochastic high‐order nonlinear systems under arbitrary switchings. Based on the common Lyapunov function and using the inductive method, virtual controllers are designed step by step and the form of the input signal of the system is constructed at the last. The unknown parameters are addressed by the tuning function method. In particular, both the designed state feedback controller and the adaptive law are independent of switching signals. Based on the designed controller, the boundness of the state variables can be guaranteed in probability. Furthermore, without considering the Wiener process or with the known parameter in the assumption, adaptive finite‐time stabilization and finite‐time stabilization in probability can be obtained, respectively. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.