广义双线性系统的残差产生器设计

Design of Residual Generator for Singular Bilinear Systems

针对具有不可测外界干扰和有界控制输入的广义双线性系统,提出了一种用于故障检测的未知输入残差产生器的设计方法。首先,通过非奇异线性变换,将广义双线性系统分解成动态和静态两个子系统,设计了未知输入残差产生器,给出了未知输入残差产生器存在的充分必要条件,并基于Lyapunov稳定理论,分析了所设计的未知输入残差产生器的指数稳定性。然后,针对未知输入残差产生器中的待定参数,基于线性矩阵不等式技术和广义逆理论,给出了未知参数的求解过程,该求解方法不需要对待求参数进行参数化的过程,易于计算。

A method to design an unknown input residual generator(UIRG) for fault detection is investigated based on Lyapunov approach for singular bilinear systems(SBS) subject to unmeasurable disturbances and bounded control inputs.By nonsingular linear transformation,the SBS is decomposed into two subsystems: dynamic system and static system.Then an UIRG is designed and a necessary and sufficient condition guaranteeing the stability and existence of the UIRG is presented.The designed UIRG is proved to be exponentially stable based on Lyapunov theory.For the parameters to be designed in UIRG,a solving procedure is derived based on linear matrix inequality technique and generalized inverse theory.The solving procedure is easy to be implemented and does not require the parameterization needed in some literatures.