Counterexample and correction to a recent result on robust stability of a diamond of complex polynomials

摘要

In a recent paper by N.K. Bose and K.D. Kim (see ibid., vol.36, p.1165-74, 1989), a main focal point is (strict left half plane) stability of a family of polynomials having complex coefficients with their real and imaginary parts each lying in a diamond. Subsequently, Bose and Kim provide a list of 16 distinguished edges of the diamond and claim that stability of these critical edges is both necessary and sufficient for stability of the entire family. In the present work, it is shown via counterexample that these 16-edge polynomials are wrongly selected. A different set of 16 edges that suffice is introduced.