Adaptive filter backstepping control for pure‐feedback nonlinear systems with quantized states

In this article, an adaptive fuzzy control strategy for pure‐feedback nonlinear systems with state quantization is proposed. The virtual and actual controllers receive quantized states, rendering them discontinuous. To address this problem, by using the command‐filtering‐based backstepping technique, auxiliary intermediate controllers are first designed with unquantized states then by substituting quantized states to obtain intermediate and actual controllers. To compensate for the impact of quantization errors, Lemma 2 is introduced. On this basis, the proposed strategy ensures the semiglobally ultimate boundedness of signals and guarantees that the output signal converges to a neighborhood of the reference signal. Eventually, a practical example is used to demonstrate the effectiveness of our proposed approach.