Fast finite-time stabilization of switched stochastic low-order nonlinear systems with asymmetric time-varying output constraints

This paper investigates the problem of fast finite-time stabilization for switched stochastic low-order nonlinear systems (SSLNSs) with time-varying powers and output constraints. Firstly, we establish a Lyapunov criterion on fast finite-time stability for switched stochastic nonlinear systems (SSNSs). By dividing the operating time into several intervals and analyzing the system’s performance within each interval, the challenges introduced by deterministic switching signals are effectively addressed. Secondly, an asymmetric nonlinear mapping (ANM) is proposed to deal with asymmetric time-varying output constraints. The ANM method overcomes the limitation of barrier Lyapunov function (BLF) method by circumventing the challenge of radial unboundedness associated with BLFs, providing an innovative solution for stabilizing non-Lipschitzian stochastic systems subject to output constraints. Finally, a fast finite-time controller (fast FTCr) incorporating two distinct power terms is designed for a class of SSLNSs. The uncertainties associated with time-varying powers are addressed, and the objective of fast finite-time stabilization is also successfully realized. The efficacy of the proposed control strategy is validated through numerical and simulation examples.