Quantization Behaviors in Equivalent-Control Based Sliding-Mode Control Systems

In this chapter, we study the quantization behaviors of the equivalent control based second order single-input sliding-mode control (SMC) systems in the presence of quantized state feedback.We show that the class of SMC systems with both uniform and logarithmic quantizers can make the system states converge into a band, which relates to the quantization parameters. Properties of the system trajectories with quantized state feedback are characterized by using the concepts of quantized sliding mode (QSM) and quantized sliding-mode control (QSMC) system. We show that the QSM is piecewise constant. Various simulations illustrate the behaviors of the equivalent-control based SMC system under uniform and logarithmic quantized state feedback.