基于一种分数时滞状态闭环泛函的量化采样系统稳定性分析

Stability analysis for sampled-data systems with quantization based on a fractional delay state looped function

对量化采样系统的稳定性问题进行研究。首先,基于Lyapunov-Krasovskii稳定性分析理论,通过在量化采样系统的采样区间内定义1个分数时滞状态,建立1个新的状态空间模型。其次,构造1个全新的分数时滞状态闭环泛函,这种泛函充分利用从tk到t-λμ(t)、从t-λμ(t)到t和从t到tk+1的区间状态信息。然后,根据这种新颖的分数时滞状态闭环泛函、用来估计泛函导数的二阶广义自由权积分不等式和一些含自由权矩阵的恒零等式,得出有量化和无量化采样系统的稳定判据。研究结果表明:基于分数时滞状态闭环泛函所得到的稳定性判据具有较低的保守性。

The stability problem for sampled-data systems with quantization was studied. Firstly, based on the Lyapunov-Krasovskii stability analysis theory, a new state space model was established by defining a fractional delay state in the sampling interval of sampled-data system with quantization. Secondly, a new fractional delay state looped function was constructed for the sampled-data system, which fully utilized the state information from tkto t-λμ(t), t-λμ(t) to t and t to tk+1. Based on this new looped functional of fractional delay state function,two-order generalized free weight integral inequality for estimating function derivatives and some constant-zero equations with free weight matrix, two asymptotic stability criteria for quantization and non-quantization of the sampled-data systems with quantization were derived. Finally, the simulation and numerical examples were used to verify the stability criteria. The results show that the obtained stability criterions based on the fractional delay state looped function are less conservative.