Abstract
In this work, a graph theoretic approach is proposed to design a static state feedback control for small scale (two or three states) structured descriptor systems. Corresponding to the system matrices and feedback gain vector, a square matrix is defined, which then allows to represent the closed system by a directed graph (digraph). It is shown that the coefficient of closed loop characteristic polynomial can be determined by using the spanning cycle families of resulting digraph. To assign the finite poles of closed loop system at some desired locations in the complex plane, a graph theoretic sufficient condition is proposed, where one needs to check the existence of spanning cycle family of a digraph. The developed algorithm is demonstrated with a numerical example.
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