The Stability of Nonlinear Dissipative Systems

IEEE Transactions on Automatic Control

Volumn 21, Issue 5, 1976, Pages 708-711

  Hill, David ^a   Moylan, Peter ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

SYSTEM STABILITY - LYAPUNOV METHODS;

CONTROL SYSTEMS, NONLINEAR;

EID: 0017009905     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1976.1101352     Document Type: Article

References (11)

1. P. J. Moylan “Implications of passivity in a class of nonlinear systems,” IEEE Trans. Automat. Contr., vol. AC-19, pp. 373–381, Aug. 1974.
2. B. D. Anderson “A system theory criterion for positive real matrices,” SIAM J. Contr., vol. 5, pp. 171–182, May 1967.
3. P. J. Moylan and B. D. Anderson “Nonlinear regulator theory and an inverse optimal control problem,” IEEE Trans. Automat. Contr., vol. AC-18, pp. 460–465, Dec. 1973.
4. J. C. Willems “Dissipative dynamical systems Part I: General theory; Part II: Linear systems with quadratic supply rates,” Arch. Rational Mechanics and Analysis, vol. 45, no. 5, pp. 321–393, 1972.
5. B. D. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis. Englewood Cliffs, NJ: Prentice-Hall, 1973.
6. J. P. LaSalle, “Dissipative systems,” in Ordinary Differential Equations 1971 NRL-MRC Conference, L. Weiss, Ed. New York: Academic, 1972.
7. A. V. Balakrishnan “On the controllability of a nonlinear System,” Proc. Nat. Acad Sci. U.S.A., vol. 55, pp. 465–468, 1966.
8. D. J. Hill and P. J. Moylan, “Cyclo-dissipativeness, dissipativeness and losslessness for nonlinear dynamical systems,” Dep. Elec. Eng., Univ. Newcastle, Newcastle, New South Wales, Australia, Tech. Rep. EE-7526, Nov. 1975.
9. J. LaSalle and S. Lefschetz, Stability by Lyapunov's Direct Method. New York: Academic, 1961.
10. J. C. Willems “The generation of Lyapunov functions for input-output stable systems,” SIAM J. Contr., vol. 9, pp. 105–134, Feb. 1971.
11. G, Zames “On the input-output stability of time-varying nonlinear feedback systems; Part I: Conditions derived using concepts of loop gain, conicity and positivity,” IEEE Trans. Automat. Contr., vol. AC-11, pp. 228–238, Apr. 1966.