Criteria for dichotomy and gradient-like behavior of a class of nonlinear systems with multiple equilibria

This paper considers global properties of a class of nonlinear systems with infinite equilibria. Time-domain and frequency-domain criteria for dichotomy and gradient-like behavior are established. Similar to the sector condition in absolute stability problems, the bounded derivative condition of nonlinear functions can be used to reduce the conservativeness of the given criteria. Compared with the frequency-domain conditions, the time-domain inequalities can be solved easily by linear matrix inequality (LMI) toolbox and used to discuss controller design problems. Several examples are given to illustrate the effectiveness of the results.