A new approach to quantized stabilization of a stochastic system with multiplicative noise

A new quantization-dependent Lyapunov function is proposed to analyze the quantized feedback stabilization problem of systems with multiplicative noise. For convenience of the proof, only a single-input case is considered (which can be generalized to a multi-input channel). Conditions for the systems to be quantized mean-square poly-quadratically stabilized are derived, and the analysis of performance and controller design is conducted for a given logarithmic quantizer. The most significant feature is the utilization of a quantization-dependent Lyapunov function, leading to less conservative results, which is shown both theoretically and through numerical examples.