The circle criterion and quadratic Lyapunov functions for stability analysis

作者: J. Willems

DOI: 10.1109/TAC.1973.1100260

关键词: Circle criterionLyapunov functionLyapunov equationJury stability criterionLyapunov redesignControl theoryStability theoryMathematicsApplied mathematicsLyapunov exponentLyapunov optimization

摘要: In this note the general equivalence is pointed out between stability results obtained by means of circle criterion and those derived from an optimum quadratic Lyapunov function.

参考文章(3)
J. Willems, Least squares stationary optimal control and the algebraic Riccati equation IEEE Transactions on Automatic Control. ,vol. 16, pp. 621- 634 ,(1971) , 10.1109/TAC.1971.1099831
R. E. Kalman, LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. Proceedings of the National Academy of Sciences of the United States of America. ,vol. 49, pp. 201- 205 ,(1963) , 10.1073/PNAS.49.2.201
A. Tsoi, H. Power, Equivalent predictions of the circle criterion and an optimum quadratic form for a second-order system IEEE Transactions on Automatic Control. ,vol. 17, pp. 565- 566 ,(1972) , 10.1109/TAC.1972.1100066