Strict Lyapunov Functions for Generating Robust Oscillations in Nonlinear Systems

This paper deals with the problem of generating stable and robust oscillations in triangular nonlinear systems. The proposed method consists of two steps. First, a globally attractive oscillation is generated in a nominal second–order subsystem. Based on a partition of the state space and solving the Lyapunov equation on each part, a strict Lyapunov function is obtained that ensures exponential convergence to a ring–shaped region containing the target limit cycle. Then, the nominal stabilizing controller and the strict Lyapunov function are extended to arbitrary order systems, via a method in the essence of backstepping. Thanks to the strict Lyapunov functions, a new ability to deal with unmodeled dynamics is acquired, and the original controller is easily extended to quasitriangular structures. Copyright c 2005 IFAC.