Asymptotic rejection for a class of switched nonlinear systems with unknown sinusoidal disturbances

This paper investigates global disturbance rejection for switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, an adaptive control methodology is established on the basis of the multiple Lyapunov functions method. Also, adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances.