Slope restrictions and monotonicity in nonlinear systems: almost linear behavior

摘要

The problems of absolute stability and existence of forced oscillations for systems with sector restricted nonlinearities are considered. An overview of the results for systems described by ordinary differential equations with constant and periodic coefficients is presented. A result is obtained on exponential absolute stability for systems described by ordinary differential equations. Next, a theorem of Persidskii type, showing that uniform asymptotic stability implies exponential stability, is obtained for a rather general class of nonlinear time varying functional differential equations. The paper ends with some problems awaiting solutions.