EXPANSION OF SOLUTION TO A ROBOT MODEL WITH TIME DELAY
带时滞机器人模型解的展开

This paper is devoted to research of solution properties of a robot model with time delay, which is described by a retarded functional differential equations. At first the equations are transformed into an evolutionary equation in the Hilbert state space, and the well-posed-ness of the system is obtained by using the theory of $C_0$ semigroup. Then, by a detail spectral analysis, the asymptotic expression of all eigenvalues of the system operator is given, and it is shown that the eigenfunctions of the system operator fail to form a Schauder basis for the state space. However, it is proven that the solution of system can be explicitly expressed via its eigenvectors when $t>5\tau$, where $\tau$ is the delay time.