Modified Mikhailov plots for robust absolute stability with non-parametric perturbations and uncertain nonlinearity

REFERENCES

• BARMISH , B. R. , 1989 , A generalization of Kharitonov's four polynomial concept for robust stability problems with linearly dependent coefficient perturbations . IEEE Transactions on Automatic Control , 34 , 1577 – 165 .
   Google Scholar
• CHEN , M. J. , and DESOER , C. A. , 1982 , Necessary and sufficient conditions for robust stability of linear distributed feedback systems . International Journal of Control , 35 , 255 – 267 .
   Web of Science ®Google Scholar
• CHEMER , L. , 1947 , Ein neues verfahren zur beurteilung der stabilitöt linearer regelungssysteme . Zeitschrift fur Angewandte Mathematiks und Mechaniks , 25/27 , 161 – 163 .
   Google Scholar
• Fu , M. , 1989 , Polytopes of polynomials with zeros in a prescribed region New criteria and algorithms . Robustness in Identification and Control , edited by M. Milanese , R. Tempo and A. Vicino ( Plenum Press ).
   Google Scholar
• GANTMACHER , F. R. , 1954 , The Theory of Matrices , Vol. 2 ( New York : Chelsea ).
   Google Scholar
• KHARITONOV , V. L. , 1978 , Asymptotic stability of an equilibrium position of a family of systems of linear differential equations . Differentsial'nye Uravneniya , 14 , 2086 – 2088 , (in Russian). English Translation 1979, Differential Equations, 14, 1483–1485 .
   Google Scholar
• KWAKERNAAK , H. , 1983 , Robustness optimization of linear feedback systems . Proceedings of the 22th IEEE Conference on Decision and Control , San Antonio , Texas .
   Google Scholar
• LEONHARD , A. , 1944 , Neues verfahren zur stabilitätsuntersuchung . Archiv für Electrotechnik , 38 , 17 – 28 .
   Google Scholar
• MIKHAILOV , A. V. , 1938 , Method for harmonic analysis in the theory of controllers . Avtom i Telemekh 3 , 27 – 81 ( in Russian ).
   Google Scholar
• MINNICHELLI , R. J. , ANAGNOST , J. J. , and DESOER , C. A. , 1989 , An elementary proof of Kharitonov's stability theorem with extensions . IEEE Transactions on Automatic Control , 34 , 995 – 998 .
   Web of Science ®Google Scholar
• NARENDRA , K. S. , and TAYLOR , J. H. , 1973 , Frequency Domain Criteria for Absolute Stability ( New York : Academic Press ).
   Google Scholar
• POPOV , V. M. , 1973 Hyperstability of Control Systems ( New York : Springer-Verlag ).
   Google Scholar
• TSYPKIN , Y. Z. , and POLYAK , B. T. , 1991 , Frequency domain criterion for robust stability of polytopes of polynomials . Control of Uncertain Dynamic Systems , edited by S. P. Bhattacharyya and L. H. Keel ( CRC Press ); 1992, Frequency domain criteria for l p-robust stability of continuous linear systems. IEEE Transactions on Automatic Control, 36, 1464–1469; 1993, Robust absolute stability of continuous systems. Journal of Robust Nonlinear Control, submitted for publication .
   Google Scholar
• VIDYASAGAR , M. , 1985 , Control System Synthesis-a Factorization Approach ( Cambridge , Mass : MIT Press ).
   Google Scholar