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Analysis of a Chain of Integrators with Pulse-Width-Modulation Controller

In application, many controllers are implemented through Pulse-Width-Modulation (PWM). Owing to the non-linearity and discontinuity of PWM signal, the closed-loop stability analysis is challenging even for linear systems. In this paper, we investigate the stability problem for a linear chain of integrators with PWM controller. Different from the existing works, the proposed procedure is developed based on Zero-Order-Hold (ZOH) and we prove that the system is stable when the switching period of the PWM signal is small enough. Simulation results of 1-order and 2-order systems demonstrate the effectiveness of the proposed method.