Global adaptive stabilization of stochastic high-order switched nonlinear non-lower triangular systems

This paper aims to deal with the global adaptive stabilization problem for a class of uncertain stochastic high-order switched nonlinear systems. The most distinctive feature of the studied system is that all drift terms of each subsystem are non-lower triangular nonlinear functions. To achieve the control objective, the retrogressed form of the studied system is first considered and a common state-feedback controller of all subsystems is first systematically constructed in the framework of the common Lyapunov function (CLF) method combined with the adding a power integrator technique, which assures the global stability in probability of the corresponding closed-loop retrogressed system under arbitrary switching. Then a sufficient condition is deliberately proposed by designing a state-dependent switching law in combination with the common state-feedback controller to ensure that the system states can be regulated to the origin almost surely and the globally stability in probability of the whole closed-loop system. Finally, two simulation examples are given to illustrate the effectiveness of the presented control schemes.