Dynamical discontinuous feedback control of nonlinear systems

An averaging technique is introduced for the accurate description of discontinuous feedback-interconnected nonlinear systems under a pulse-width-modulation (PWM) scheme for the switching element. The averaging process is based on an infinite-switching-frequency assumption on the feedback-enabling device. The proposed average model is shown to capture entirely the main qualitative and quantitative features of the actual finite-frequency-switched controlled system. The existence of a sliding motion in the augmented state space of the closed-loop pulsed-controlled system, which closely follows the average trajectories, makes the approximation scheme amenable to arbitrary improvement under increased switching frequency specifications for the actual controlled system. This entirely obviates the need for cumbersome approximation schemes based on traditional discrete-time considerations and the technical difficulties associated with the unbounded character of the PWM operator.<>