离散广义双线性系统的稳定控制分析

Stable controlling analysis for discrete singular bilinear systems

讨论了离散广义双线性系统稳定控制问题。研究了离散广义双线性系统稳定控制存在的条件,并给出了相应的控制方案。所采用的方法是利用广义系统分解,运用Lyapunov方法证明线性状态控制可以使闭环系统在原点附近渐近稳定。同时研究了不分解系统,通过构造广义李雅普诺夫函数的方法,给出了使闭环系统稳定的条件。对于离散广义双线性系统有关理论的证明,可以看作是正常离散双线性系统的拓广。

The stability problem for a discrete singular bilinear system is investigated. The existing conditions of stable controlling for discrete singular bilinear systems are studied and the corresponding controlling scheme is given. By decomposing the singular system and applying Lyapunov method, it is proved that linear state control can make a closed loop system asymptotically stable around the origin. By constructing singular Lyapunov function, the conditions of making a closed loop system stable under the condition not decomposing the system are also researched. The proof of the relevant theory for the discrete singular bilinear system may be regarded as the extension of the normal discrete bilinear system.