线性多输入系统可控性判断的快速算法

Fast algorithm of judging the controllability in the time-invariant linear system

讨论了定常线性系统的可控性矩阵秩的性质,指出对输入矩阵施行列初等变换不改变系统的可控性,给出了判断定常线性多输入系统可控性的一种快速算法及其改进算法,证明了最多只需经过[log2(n-k)]+1步迭代便可判断其可控性,而当迭代矩阵的秩没有增加时便可断定其不可控,从而使计算步骤大大减少,并且容易在计算机上实现.

After the discussion of the properties of the rank of controllable matrix in time-invariant linear system, it is inferred that the controllability is not changed when elementary column operation is performed on the input-matrix. A fast algorithm of judging the controllability in the system and its improvement were deduced by using the elementary column transformation on the controllable matrix. It is proved that judging the controllability in the system need at most +1 iteration algorithm and the system is not controllable when the rank of the iteration matrix is not added. This fast algorithm is easy to compute the rank of the controllable matrix and is feasible to be realized in the computer.