For this study, we interpreted the first

characteristic root only (see Table 2).

It not only effectively decreases the grid current distortion and control delay but also improves the system stability and dynamic response speed due to reducing the

characteristic root equation order of the closed-loop transfer function.

Without loss of generality, we assume that uniquely

characteristic root is zero and the first invariant factor of the matrix F(x) is unit.

where [[lambda].sub.g] (g = 1, 2, ...m) is the

characteristic root, which is the variance of principal component.

The

characteristic root of matrix (18) is located within the unit circle on the complex plane, and it can be seen that the internal equilibrium point of the controlled system (18) is stable under the settled parameter values, and the chaotic motion of system (6) can also be adjusted to the expected stable orbit, and it can consequently reach the value range of feedback gain intensity.

As has been analyzed in Section 3.1,

characteristic root has relationship with the value of [DELTA].

Roots attacked by root knot nematodes exhibit

characteristic root galls, and infected plants grow poorly or even die because of poor nutrient intake and vascular dysfunction.

Let a be the

characteristic root of the multiplicity n of matrix A(x) of the form (2).

Characteristic root value is an index to evaluate the influence of extracted common factors; that is, introduction of this common factor can explain and evaluate the information of the original variables.

Hence, one

characteristic root is the solution of the equation

Apparently, the

characteristic root of characteristic equation (9) is [[lambda].sub.1] =-[mu]< 0, thus the stability of [E.sup.+] is determined by the signs of root in the following equation:

In particular, a primitive matrix is an irreducible nonnegative matrix with g = 1, it has exactly one dominant

characteristic root. We find that, for 3 [less than or equal to] m [less than or equal to] 10, the transfer matrix [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is irreducible, but it is primitive only when m is even.