Analysis of oscillation and stability for systems with piecewise linear components via saturation functions

This paper develops a unified Lyapunov approach to analysis of self-induced oscillations and stability for systems with piecewise linear components. For self-induced oscillation within a global or regional attractor, invariant level sets of a piecewise quadratic Lyapunov function are obtained to bound the attractor via linear matrix inequality based optimization. The analysis results for self-induced oscillations are easily adapted to global or regional stability analysis.