具有量化误差的非线性多步长采样系统的稳定性

研究具有量化误差的非线性多步长采样系统的稳定性．证明了无量化误差的线性化采样系统的系数矩阵在Schur稳定的条件下,原非线性采样系统是一致渐近稳定的；而具有量化误差的非线性采样系统在一致终极有界的意义下是稳定的；同时证明两者之间响应的差异,当量化误差趋于零时而趋于零．

Multirate Sampled-Data Stability of Nonlinear Systems with Quantization

This paper studies the stability of multirate sampled-data nonlinear systems with quantization. Under the assumption of the Schur stability of the coefficient matrix for its linearized sampled-data systems without quantization, we have shown that the multirate sampled-data systems without quantization is uniformly asymptotic stable and the multirate sampled-data systems with the constrained quantization is stable in the sense of the uniform ultimate boundedness. Finally, the difference in the response of the multirate sampled-data systems with no quantization and the systems with quantization can be made as small as desired by selecting the quantization level sufficiently small.