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References in periodicals archive ?
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 [7].
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.
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