On Absolute Stabilization of the Lur'e Nonlinear System

This Paper is concerned with the absolute stabilization of the Lur'e nonlinear system. A set of necessary and sufficient conditions of absolute stabilizability by a linear state feedback (LSF) via a quadratic Lyapunov function (QLF) are derived. One class of LSF controls is meanwhile constructed for stabilizing the system. We also present several algorithms for testing the stabilizability and constructing the stabilizing control law.