Fixed-time stabilisation for switched stochastic nonlinear systems with asymmetric output constraints

In this paper, the fixed-time stabilisation problem is investigated for switched stochastic nonlinear systems with asymmetric output constraints. A novel universal barrier Lyapunov function is proposed to not only handle systems with asymmetric output constraints but also work for systems with symmetric constraints or without constraints, without reshaping the controller framework. On the basis of the stochastic fixed-time stability theorem and adding a power integrator strategy, an elaborate control method is established to ensure that the system state fixed-time converges to zero almost surely without the knowledge of initial conditions. Meanwhile, the system output is always retained in the preset asymmetric region in probability. A practical example is utilised to verify the validity of the proposed theory.