Absolute stability criteria for multiple slope-restricted monotonic nonlinearities

Absolute stability criteria such as the classical Popov criterion guarantee stability for a class of sector-bounded nonlinearities. Although the sector restriction bounds the admissible class of the nonlinearities, the local slope of the nonlinearity may be arbitrarily large. In this paper the authors derive absolute stability criteria for multiple slope-restricted time-invariant monotonic nonlinearities. Like the Popov criterion, in the single-input/single-output case the authors' results provide a simple graphical interpretation involving a straight line in a modified Popov plane. >

[1]  B. Anderson,et al.  A generalization of the Popov criterion , 1968 .

[2]  D. Bernstein,et al.  Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory , 1993 .

[3]  D. Bernstein,et al.  Parameter-dependent Lyapunov functions, constant real parameter uncertainty, and the Popov criterion in robust analysis and synthesis. 2 , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[4]  Dennis S. Bernstein,et al.  Extensions of mixed-µ bounds to monotonic and odd monotonic nonlinearities using absolute stability theory† , 1994 .

[5]  K. Narendra,et al.  Stability of a Class of Differential Equations with a Single Monotone Nonlinearity , 1966 .

[6]  M. Srinath,et al.  Some aspects of the Lur'e problem , 1967, IEEE Transactions on Automatic Control.

[7]  Kinetic Lyapunov Function for Stability Analysis of Nonlinear Control Systems , 1961 .

[8]  D. Bernstein,et al.  Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis , 1995, IEEE Trans. Autom. Control..

[9]  C. P. Neuman,et al.  Stability of continuous time dynamical systems with m-feedback nonlinearities. , 1967 .

[10]  E. Jury,et al.  A stability inequality for a class of nonlinear feedback systems , 1966 .

[11]  M. Safonov.  Stability of interconnected systems having slope-bounded nonlinearities , 1984 .

[12]  J. Wen.  Time domain and frequency domain conditions for strict positive realness , 1988 .

[13]  D. Bernstein,et al.  Extensions of mixed- mu bounds to monotonic and odd monotonic nonlinearities using absolute stability theory. I , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

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

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

[16]  Dennis S. Bernstein,et al.  Off-axis absolute stability criteria and μ-bounds involving non-positive-real plant-dependent multipliers for robust stability and performance with locally slope-restricted monotonic nonlinearities , 1993, 1993 American Control Conference.

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