Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers

In this paper, we will present new results on global finite-time stabilization for a class of switched strict-feedback nonlinear systems, whose subsystems have chained integrators with the powers of positive odd rational numbers (i.e., numerators and denominators of the powers are all positive odd integers but not necessarily relatively prime). All the powers in each equation of subsystems of the switched systems can be different. Based on the technique of adding a power integrator, the global finite-time stabilizers of individual subsystems are first systematically constructed to guarantee global finite-time stability of the closed-loop smooth switched system under arbitrary switchings, and then a co-design of stabilizers and a state-dependent switching law is proposed to achieve global finite-time stabilization of the closed-loop non-smooth switched systems. In the controller design, a common coordinate transformation of all subsystems is exploited to avoid using individual coordinate transformations for individual subsystems. We also give some sufficient conditions that enable our design by characterizing the powers of the chained integrators of the considered switched systems. Numerical examples are provided to demonstrate the effectiveness of the proposed results.