Prescribed-Time Stabilization of Uncertain Planar Nonlinear Systems with Output Constraints

This brief reports the prescribed-time stabilization (PST) problem for a class of uncertain planar nonlinear systems with output constraints. To handle the obstacle caused by the output constraints, a tan-type Barrier Lyapunov Function (BLF) that equates to the classical one for unconstrained systems is exploited. By suitably introducing the time-varying function into the virtual (actual) controllers rather than conventionally to scale the coordinate transformations, a switched, non-scaling design scheme for state feedback is developed to ensure that the origin of the resulting closed-loop system (CLS) is prescribed-time stable without disobeying the constraints. The novelty of the proposed control strategy is that it solves the computationally singular problem effectively and leads to a simpler controller in comparison with the traditional scaling design. Finally, the appealing performance of the proposed scheme is illustrated by simulation.