Estimation of Magnitude of Self-Induced Oscillations via Piecewise Quadratic Lyapunov Functions

A Lyapunov approach is developed in this paper for estimation of the magnitude of self-induced oscillations for systems with piecewise linear elements. The oscillatory trajectories are bounded by invariant level sets of a piecewise quadratic Lyapunov function. An optimization problem with bilinear-matrix-inequality constraints is formulated to minimize the invariant level set and to obtain tight bound for oscillatory trajectories. Several examples demonstrate the effectiveness of the new method on analysis of self-induced oscillations.