The closed-loop characteristic polynomial
[A.sub.c] thus can be rewritten as
The desired closed-loop characteristic polynomial
is [z.sup.2] - 1.2131z + 0.3679 for Eq 10.
The following robust stability tests of the resulting closed-loop characteristic polynomials with affine linear uncertainty structure utilize the combination of the value set concept and the zero exclusion principle .
Then, the related family of closed-loop characteristic polynomials is:
The corresponding family of closed-loop characteristic polynomials with parameters from (11) is:
Then, the expression of closed-loop characteristic polynomial
and setting the real and imaginary parts to zero lead to the equations:
As the stability of LTI systems can be investigated via the stability of its characteristic polynomials, the primary object of interest from the robust stability viewpoint is the family of closed-loop characteristic polynomials
. Besides, if the controlled plant model contains time delay term, the family of closed-loop characteristic quasipolynomials has to be analyzed.
stabilizes the interval plant (7) [a.sub.ij] [member of ] ([a.sup.+.sub.ij], [a.sup.-.sub.ij]) if the coefficient vectors of the closed-loop characteristic polynomials
[f.sup.+.sub.ij] of all the corner plants are placed in the polytope of reflection vectors [v.sup.+.sub.ij](f), [alpha] = 1, ..., n of the nominal closed-loop system f.