广义线性系统的鲁棒镇定分析

Robust Stabilization Analysis for Singular Linear Systems

系统的鲁棒控制在工程控制的实际问题中有着广泛的应用 ,其研究受到人们的普遍关注。同时由于实际问题需要用广义系统模型才能加以准确地描述 ,因此 ,广义系统的鲁棒控制问题有着重要的实际意义。此外 ,广义系统的结构比通常系统的结构要复杂的多 ,采用通常的方法分析广义系统的鲁棒控制显得十分困难 ,正基于此 ,加强对广义系统的鲁棒控制分析十分必要。基于Lyapunov方程和Riccati方程分析了确定性广义线性系统的鲁棒镇定问题 ,得出了不带输入项的正则无脉冲的广义线性系统的零解渐近稳定的充分必要条件和带有输入项的正则无脉冲的广义线性系统的零解渐近稳定的充分必要条件。对于带有输入项的广义线性系统 ,可通过调整二次型指标函数中的加权阵便可方便调整系统的动态稳定性指标。

Robust control for system has been widely applied in solving practical engineering problems, and great attention has been drawn by its deep researches. At the same time, the practical engineering problems can be described precisely by using the singular system model, so it is very necessary for discussing the robust control of singular systems. In addition, the structure of singular system is more complex than that of normal systems and it is difficult to use the normal methods to deal with the robust control for singular systems. Accordingly, it is important to emphasize the research on the robust control for singular systems. In this paper, robust stabilization of definitive singular linear systems has been analyzed based on Lyapunov equation and Riccati equation of singular linear systems.The sufficient and necessary conditions of the zero-solution gradual stability for proper and pulseless singular system without input term has been achieved. Meanwhile, the sufficient and necessary conditions of the zero-solution gradual stability for proper and pulseless singular system with input term has been achieved, too. For the singular system with input term, it is convenient to adjust the dynamic robust stable index by regulating the weight matrices in the quadratic performance index function.