Adaptive Absolute Stability∗

A new property of adaptive absolute stability for nonlinear Lurie systems is introduced. Adaptive absolute stability is an extension of classical absolute stability or Lurie problem. An algorithm of adaptive absolute stabilization based on new Passification theorem is proposed. It is shown that the proposed conditions for adaptive absolute stability are equivalent to existence of quadratic Lyapunov function of special class. The theoretic results of the paper are illustrated by example.