A New Approach to Quantized Stabilization of Stochastic System with Multiplicative Noise

A new quantization dependent Lyapunov function is proposed to analysis the quantized feedback stabilization problem of discrete-time system with multiplicative noises. For convenience of the proof, only single-input case is considered (which can be generalized to multi-input channel), conditions for the system to be mean-square poly-quadratic stabilized are derived as well as the analysis of H
∞
performance and controller design for the given stochastic system with 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.