基于量化控制的网络系统稳定性分析

Stability analysis for network system based on quantitative control

研究一类带有量化的网络控制系统的渐进稳定性问题。首先,根据线性网络控制系统的特点和一类对数量化器的扇形有界条件,建立1个网络控制系统的静态量化模型;然后,针对所建立的静态量化模型,基于Lyapunov?Krasovskii(L?K)稳定性分析理论,通过构建1个全新的增广L?K泛函,采用1个由贝塞尔?勒让得(B?L)积分不等式和基于函数的辅助型积分不等式衍生而来的新积分不等式,该不等式能够更加与构建的泛函紧密相结合;运用逆凸技术和含自由权矩阵的恒零等式,获得1个少保守性的渐进稳定性新判据;最后,通过数值实例进行仿真研究。研究结果表明:新的增广L?K泛函和新积分不等式能够使得到的渐进稳定性判据较优且有效。

The asymptotic stability of a class of network control system with quantization was studied.Firstly,according to the characteristics of linear network control system and the sector bounded condition of a class of logarithmic quantizer,a static quantization model of network control system was established.Secondly,based on the Lyapunov?Krasovskii(L?K)stability analysis theory,a new asymptotic stability criterion of the less conservative was obtained by constructing a novel augmented L?K functional.By using the reciprocally convex approach and the constant zero equality with free-weighting matrix and the new integral inequality,the new integral inequality was derived from the Bessel-Legendre(B?L)integral inequality and the auxiliary functionbased integral inequality,which could be more closely combined with the constructed functional.Finally,simulation was conducted with numerical examples.The results show that the new augmented L?K functional and the new integral inequality can make the obtained asymptotic stability criteria better,and the criterion is effective.