Generalization and comparison of two recent frequency-domain stability robustness results

References

• ARGOUN , M. B. , 1987 a, Stability of a Hurwitz polynomial under coefficient perturbations: necessary and sufficient conditions. International Journal of Control 45 , 739 – 744 ; 1987b, Frequency domain conditions for the stability of perturbed polynomials I. E. E. E. Transactions on Automatic Control , 32, 913-916; 1990, On the stability of low order perturbed polynomials Ibid., 35, 180-182.
   Google Scholar
• BARMlsH , B. R. , 1984 , Invariance of the strict Hurwitz properly for polynomials with perturbed coefficients. I. E. E. E. Transactions on Automatic Control , 29 , 935 – 936 ; 1989, A generalization of Kharitonov's four polynomial concept for robust stability problems with linearly dependent coefficient perturbations. Ibid., 34, 157-165.
   Google Scholar
• BIALAS , S. , and GARLOFF , J. , 1985 , Stability of polynomials under coefficient perturbations. I. E. E. E. Transactions on Automatic Control , 30 , 310 – 312 .
   Google Scholar
• BISTRITZ , Y. , 1988 , Stability criterion for continuous-time system polynomials with uncertain complex coefficients. I. E. E. E. Transactions on Circuits and Systems , 35 , 442 – 448 .
   Google Scholar
• BOSE , N. K. , JURY , E. I. , and ZEHEB , E. , 1988 , On robust Hurwitz and Schur polynomials. I. E. E. E. Transactions on Automatic Control , 33 , 1166 – 1168 .
   Web of Science ®Google Scholar
• BOSE , N. K. , and SHI Y. Q. , 1987 , A simple general proof of Kharitonov's generalized stability criterion. I. E. E. E. Transactions on Circuits and Systems , 34 , 1233 – 1237 .
   Google Scholar
• Fu , M. , and BARMISH , B. R. , 1988 , Maximal unidirectional perturbation bounds for stability of polynomials and matrices. Systems and Control Letters , 11 , 173 – 179 .
   Web of Science ®Google Scholar
• JURY , E. I. , 1982 , Inners and Stability of Dynamic Systems , second edition ( Malabar , Fla : Krieger ), p. 32 .
   Google Scholar
• KHARITONOV , V. L. , 1978 a, Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differential Equations , 14 , 1483 – 1485 ; 1978b, On a generalization of a stability criterion. Izvestiya Akademii Nauk Kazakhskogo SSR Seriya Fizika Materialy 1, 53-57 (in Russian).
   Google Scholar
• LIPATOV , A. V. , and SOKOLOV , I. , 1979 , Some sufficient conditions for stability and instability of continuous linear stationary systems. Automation and Remote Control , 39 , 1285 – 1291 (translated from Automatika i Telemekhanika, 9, 30-37.
   Web of Science ®Google Scholar
• MINNICHELLI , R. J. , ANAGNOST , J. J. , and DESOER , C. A. , 1989 , An elementary proof of Kharitonov stability theorem with extensions. I. E. E. E. Transactions on Automatic Control , 34 , 995 – 998 .
   Web of Science ®Google Scholar
• MORI , T. , and KOKAME , H. , 1989 , Extended Kharitonov theorems and their applications. Proceedings of the American Control Conference , (ACC-89) Pittsburgh , Pennsylvania , pp. 627 – 632 .
   Google Scholar
• POLAK , E. , 1964 , A note on V-decomposition Theory. I. E. E. E. Transactions on Automatic Control , 9 , 107 – 109 .
   Google Scholar
• SOH , C. B. , 1990 , Generalization of the Hermite- Biehler theorem and application. I. E. E. E. Transactions on Automatic Control , 35 , 222 – 225 .
   Google Scholar
• SOH , C. B. , BERGER , C. S. , and DARKE , K. P. , 1985 , On the stability properties of polynomials with perturbed coefficients. I. E. E. E. Transactions on Automatic Control , 30 , 1033 – 1036 .
   Web of Science ®Google Scholar
• TSYPKIN , Ya. Z. , and POLYAK , B. T. , 1991 , Frequency-domain criterion for Ip-robust stability of continuous linear systems. I. E. E. E. Transactions on Automatic Control , to be published.
   Google Scholar
• VICINO , A. , 1988 , Some results on robust stability of discrete-time systems. I. E. E. E. Transactions on Automatic Control , 33 , 844 – 847 .
   Google Scholar
• YEUNG , K. S. , 1983 , Linear system stability under parameter uncertainties. International Journal of Control , 38 , 459 – 464 .
   Web of Science ®Google Scholar