A method for smoothing of discontinuous controller

In a control design, a switching controller is known to be a useful method that has a good robustness and stabilizes a nonlinear system with uncertainty. However, in despite of the theoretical worth as a control strategy, some practical problems such as chattering phenomenon by switching action have been also reported. With the background, many kinds of attenuation methods for a hard switching action have been proposed. In general, since there are a trade-off between a control performance and an attenuation of switching, introduction of a simple smoothing method may result in unacceptable degradation of control performance. Especially, a method that assures asymptotic stability of a closed loop system with a smoothed switching controller is desired. In this paper, we propose a new smoothing method for a switching controller where a class of nonlinear systems with a discontinuous uncertainty, which satisfies the matching condition with respect to a control input, is considered and a L_gV structure-based switching controller is employed as a target controller to be smoothed. The development of our smoothing method is based on the Filippov´s framework and the generalized Lyapunov stability theory, and in order to attenuate a hard switching action, we modify the switching controller by adding an integrator as a new internal state. We show an attractiveness and a boundedness of a controlled system by directly analyzing the generalized time derivative of a Lyapunov-like function.