Finite-time stabilisation for a class of high-order uncertain planar systems with an output constraint via output feedback

This article is concerned with the output-feedback finite-time stabilisation problem for a class of high-order planar systems with unknown control coefficients, unknown measurement sensitivity and output constraint. The bounds of the unknown control coefficients and unknown measurement sensitivity are unknown, which prevent the construction of conventional constrained output-feedback finite-time controllers. Based on homogeneous systems theory, a simple constrained output-feedback finite-time controller is successfully constructed by utilising a new type of barrier Lyapunov function. Rigorous theoretical analysis suggests that the considered system under the proposed output-feedback controller is finite-time stable, and the requirement of output constraint is achieved. The innovative aspect of this control approach is its unification of the output-feedback finite-time stabilisation problem for high-order uncertain planar systems, addressing both scenarios with and without output constraints, all within a unified framework, without altering the established control structure. Finally, two examples are given to illustrate the effectiveness of the proposed control scheme.