Fixed-time output feedback stabilization for second-order switched systems with output constraints

In this paper, the problem of fixed-time output feedback stabilization for second-order switched nonlinear systems with output constraints is investigated. Reduced-order switched state observers are constructed deliberately to estimate the unmeasured state, and by combining the switched observers with the elaborately designed switched state feedback controllers, fixed-time output feedback stabilization of the closed-loop switched systems is realized. The tangent-type barrier Lyapunov function is applied to ensure that the closed-loop switched systems can satisfy the output constraints while being stable in a fixed time. As the output constraint tends to infinity, the constructed barrier Lyapunov function degenerates into a common Lyapunov function for the case without constraints. Therefore, the method proposed in a unified framework in this paper applies to both cases with or without output constraints, with no need to change the designed structure of the switched controllers and observers. The main results in this study are proved by the bi-limit homogeneous method. Numerical simulations and fixed-time control of continuously stirred tank reactors verify the effectiveness of the proposed method.