Stabilization for a Class of Feedforward Nonlinear Systems via Pulsewidth-Modulated Controllers

This article is concerned with the stabilization problem for a class of feedforward nonlinear systems via pulsewidth-modulated (PWM) controllers. First, a state observer, which features a dynamic predictor and a jumping update, is designed such that the unavailable full system state can be accurately estimated. With the obtained state estimations, a reference signal is also constructed. Second, a three-level-state-dependent PWM controller is proposed, which switches among three prescribed states during each cycle and can be determined by two key variables, namely, the duty cycle and the sign of the pulse. It is then demonstrated that the two controller variables can be both expressed in the form of the reference signal, and the design of the controller variables depends on a key parameter that regulates the reference signal. Furthermore, it is shown that the stabilization problem can be cast into a selection problem of the key parameter. By resorting to the Lyapunov stability theory, rigorous stability analysis of the resulting closed-loop system is performed. Finally, a resonant circuit system for liquid level control and a numerical example are provided to validate the effectiveness of the proposed PWM control method.