Stability numbers for nonlinear systems

Abstract

The definition of Lyapunov stability is used for the introduction of stability numbers for nonlinear systems. A norm of the initial conditions || X 0 || and a norm of the system response || X (t)|| are related to each other, resulting in stability numbers depending on the initial conditions. This concept presents some information on the global behaviour of the system including all types of solutions from limit cycles to strange attractors. The stability numbers characterize that part of the state space in which the motion occurs.