论文信息 - Counterexample and correction to a recent result on robust stability of a diamond of complex polynomials

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

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.<<ETX>>

[1] Roberto Tempo,et al. An extreme point result of robust stability of a diamond of polynomials , 1992 .

[2] E. I. Jury,et al. Robust Schur stability of a complex-coefficient polynomials set with coefficients in a diamond , 1990 .

[3] Roberto Tempo,et al. A dual result to Kharitonov's theorem , 1990 .

[4] R. Tempo. The dual theorem of Kharitonov for a class of dependent uncertainties , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[5] Nirmal K. Bose,et al. Stability of a complex polynomial set with coefficients in a diamond and generalizations , 1989 .

[6] Roberto Tempo,et al. An extreme point result for robust stability of a diamond of polynomials , 1990, IEEE Conference on Decision and Control.

[7] Minyue Fu,et al. A class of weak Kharitonov regions for robust stability of linear uncertain systems , 1991 .

[8] A. Rantzer. Hurwitz testing sets for parallel polytopes of polynomials , 1990 .

[9] Ian R. Petersen,et al. A new extension to Kharitonov's theorem , 1987 .