Stability: the common thread in the evolution of feedback control

Advances in feedback control theory have inextricably been linked to progress in stability theory, and conversely, the horizons of stability theory have greatly been expanded by the challenges posed in increasingly complex feedback control systems. In the present article we trace the development of stability theory in feedback control by making contact with some of the major milestones in this area.

[1]  S. Lefschetz Stability of nonlinear control systems , 1966 .

[2]  M. Vidyasagar,et al.  Qualitative Analysis of Large Scale Dynamical Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Edward Wilson Kimbark,et al.  Power System Stability , 1948 .

[4]  A. Liapounoff,et al.  Problème général de la stabilité du mouvement , 1907 .

[5]  J. Maxwell I. On governors , 1868, Proceedings of the Royal Society of London.

[6]  D. Pidhayny,et al.  The origins of feedback control , 1972 .

[7]  E. Kamke Zur Theorie der Systeme gewöhnlicher Differentialgleichungen. II. , 1932 .

[8]  I. Sandberg A frequency-domain condition for the stability of feedback systems containing a single time-varying nonlinear element , 1964 .

[9]  J. Schur,et al.  Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. , 1917 .

[10]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[11]  Jan C. Willems,et al.  The Analysis of Feedback Systems , 1971 .

[12]  Mathukumalli Vidyasagar,et al.  Input-Output Analysis of Large-Scale Interconnected Systems , 1981 .

[13]  George Zames On the stability of nonlinear, time-varying feedback systems. , 1964 .

[14]  A. Hurwitz Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt , 1895 .

[15]  Dragoslav D. Šiljak,et al.  Large-Scale Dynamic Systems: Stability and Structure , 1978 .

[16]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[17]  I. W. Sandberg,et al.  On the boundedness of solutions of nonlinear integral equations , 1965 .

[18]  R. Kálmán LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Best transactions paper award of the IEEE control systems society , 1979, IEEE Circuits & Systems Magazine.

[20]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[21]  J. L. Massera Contributions to Stability Theory , 1956 .

[22]  H. Nyquist,et al.  The Regeneration Theory , 1954, Journal of Fluids Engineering.

[23]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .

[24]  I. Sandberg A Stability Criterion for Linear Networks Containing Time-Varying Capacitors , 1965 .

[25]  J. P. Lasalle,et al.  Absolute Stability of Regulator Systems , 1964 .

[26]  G. Zames On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearities , 1966 .

[27]  A. Leonhard,et al.  Neues Verfahren zur Stabilitätsuntersuchung , 1944 .

[28]  R. Bellman Vector Lyanpunov Functions , 1962 .

[29]  J. P. Lasalle Liapunov’s Direct Method , 1986 .

[30]  G. B. Airy,et al.  I. On the Regulator of the Clock-work for effecting uniform Movement of Equatoreals , 1840 .

[31]  A.N. Michel,et al.  Associative memories via artificial neural networks , 1990, IEEE Control Systems Magazine.

[32]  Wolfgang Hahn Über stabilitätserhaltende Abbildungen und Ljapunovsche Funktionen. , 1967 .

[33]  J. L. Massera On Liapounoff's Conditions of Stability , 1949 .

[34]  I. W. Sandberg,et al.  On the L 2 -boundedness of solutions of nonlinear functional equations , 1964 .

[35]  W. Evans,et al.  Graphical Analysis of Control Systems , 1948, Transactions of the American Institute of Electrical Engineers.

[36]  I. Sandberg Some results on the theory of physical systems governed by nonlinear functional equations , 1965 .

[37]  T. Ważewski,et al.  Systèmes de équations et des inégalités différentielles ordinaires aux deuxièmes membres monotones et leurs application , 1950 .

[38]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[39]  J. P. Lasalle Some Extensions of Liapunov's Second Method , 1960 .

[40]  A. Cohn,et al.  Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise , 1922 .

[41]  G. Zames On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[42]  J. P. Lasalle THE EXTENT OF ASYMPTOTIC STABILITY. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[43]  W. Hahn Theorie und Anwendung der direkten Methode von Ljapunov , 1959 .

[44]  Max b. Müller Über das Fundamentaltheorem in der Theorie der gewöhnlichen Differentialgleichungen , 1927 .

[45]  H. S. Black,et al.  Stabilized feedback amplifiers , 1934 .