矩阵指数范数的新估计方法

A New Estimating Method for the Norm fo an Exponential Matrix

放弃了稳定矩阵的指数范数的传统估计方法‖ｅＡｔ‖≤βｅ－αｔ（ｔ≥０），而采用新的估计方法‖ｅＡｔ‖≤ｃＴｅＢｔｂ（ｔ≥０）．新方法具有参数易于确定、估计精度高等优点．结合积分判据，它可应用在时变线性系统、大系统、时滞系统等问题中．

The traditional estimating method for the norm of an exponential matrix ‖e At ‖≤ β e -αt is here discarded. A new one is developed and used to investigate the stability of the time varying linear system and the large scale system. It is pointed out that the new method is also successful in the investigation of the stability of the large scale system with delay. Many examples show that the new estimating method proposed is of higher accuracy and the parameters to be taken are easily determined in practice.