关联量化系统参数稳定性与控制器设计

量化问题广泛存在于计算机控制系统和数字通信的传输通道中. 本文研究一类非线性关联量化系统的参数稳定性及分散状态反馈控制器的设计问题. 每个控制器的输出经过对数量化器量化后输入到子系统中，其量化密度的大小会影响系统的稳定性. 首先，设计分散状态反馈控制器，使得无量化器存在时的关联闭环系统参数稳定，并确定参数稳定的区域；然后，对每个子系统的控制输入采用对数量化器进行量化，通过局部信息确定子系统中对数量化器量化密度的下界，使得整个闭环关联量化系统在参数稳定域内仍然保持稳定；最后，对给定量化密度，优化控制器使系统能容许最大的非线性. 仿真结果表明，本文所设计的分散量化控制器在参数稳定域内能够镇定关联大系统.

Parametric Stability and Controller Design for Interconnected Systems with Quantization

The effect of quantization has become a big concern in the design of computer-based control systems and digital communication systems. This paper studies the analysis of parametric stability and decentralized state feedback control of a kind of interconnected systems with quantization. The output of each controller is quantized by a logarithmic quantizer before it is input to the subsystem, and the quantized density would affect the stability of the system. First, a decentralized state feedback controller is designed for interconnected systems without quantization and the corresponding stable region is obtained. Second, the lower bound of the quantization density is evaluated by local information, so that the closed-loop system is still parametrically stable. Finally, for a given quantization density, the controller is optimized to maximize the bound of the nonlinearity. Simulation results show that by using the proposed quantized controllers, the interconnected large-scaled systems are parametrically stabilized.