Adaptive Quantized Controller Design Via Backstepping and Stochastic Small-Gain Approach

This paper addresses an output feedback stabilization problem for a class of stochastic nonlinear systems with unmodeled dynamics preceded by hysteretic quantized input. To deal with unmeasurable states, a novel state observer that contains the quantized control is introduced. By presenting a new nonlinear decomposition for the hysteretic quantized input, the major technique difficulty coming from the discrete quantized input is overcome. By utilizing the backstepping technique and employing the stochastic small-gain theorem, a direct adaptive fuzzy output feedback control scheme is developed. The proposed design approach can guarantee that the closed-loop system is input-to-state practically stable in probability. Finally, a simulation example verifies the proposed control scheme.