Global stabilization design for switched power integrator triangular systems with different powers

In this paper, we will study the global exponential stabilization (GES) under arbitrary switchings for a class of switched nonlinear systems in power integrator triangular form, whose subsystems have chained integrators with the powers of positive odd numbers. Unlike the existing results on systems where the powers are assumed to be identical inẋi-equation, all the powers in each equation of subsystems of the switched systems can be different. Based on the unbounded time-varying scaling of the states, both a class of state-feedback controllers of individual subsystems and a common Lyapunov function (CLF) are explicitly constructed by a recursive design algorithm to guarantee global exponential stability of the closed-loop switched system under arbitrary switchings. In the controller design, a common transformation of all subsystems is exploited to avoid using individual coordinate transformation for each subsystem, which is achieved by establishing the relationship of the powers. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.