Stability criteria of sector- and slope-restricted Lur'e systems

Presents stability criteria of sector- and slope-restricted Lur'e systems, in terms of linear matrix inequalities, by fully exploiting inherent properties of sector and slope restrictions in the time domain. Interpreting the time-domain criteria in the frequency domain, furthermore, supplies simpler expressions. Several examples show excellent performances of these criteria.

[1]  K. Narendra,et al.  Frequency Domain Criteria for Absolute Stability , 1973 .

[2]  Aristide Halanay,et al.  Absolute stability of feedback systems with several differentiable non-linearities , 1991 .

[3]  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.

[4]  V. Singh,et al.  A stability inequality for nonlinear feedback systems with slope-restricted nonlinearity , 1984 .

[5]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1997, IEEE Trans. Autom. Control..

[6]  T. Başar Absolute Stability of Nonlinear Systems of Automatic Control , 2001 .

[7]  J. Willems,et al.  The Dissipation Inequality and the Algebraic Riccati Equation , 1991 .

[8]  J. Wen,et al.  Robustness analysis of LTI systems with structured incrementally sector bounded nonlinearities , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[9]  V. Singh Absolute stability criterion for a class of nonlinear systems with slope-restricted nonlinearity , 1982, Proceedings of the IEEE.

[10]  P. Falb,et al.  Stability Conditions for Systems with Monotone and Slope-Restricted Nonlinearities , 1968 .

[11]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[12]  J. Suykens,et al.  An absolute stability criterion for the Lur'e problem with sector and slope restricted nonlinearities , 1998 .

[13]  Vimal Singh A new approach to the absolute stability of nonlinear feedback systems with slope-restricted nonlinearity , 1985 .

[14]  P. Park A revisited Popov criterion for nonlinear Lur'e systems with sector-restrictions , 1997 .

[15]  Wassim M. Haddad,et al.  Absolute stability criteria for multiple slope-restricted monotonic nonlinearities , 1995, IEEE Trans. Autom. Control..

[16]  J. Willems,et al.  Frequency domain stability criteria--Part II , 1965 .

[17]  G. V. S. Raju,et al.  Absolute stability of control systems with many sector and slope-restricted non-linearities , 1974 .