Componentwise asymptotic stability of a class of nonlinear systems

Componentwise asymptotic stability is a special type of asymptotic stability, where each component of the state-space trajectories approaching the equilibrium point is individually monitored (unlike the standard asymptotic stability, which relies on global information about the state variables, formulated in terms of norms). This property is explored for a class of nonlinear systems, by using the theory of flow-invariant sets. Supplementary requirements for the individual evolution of the state variables approaching the equilibrium point allow introducing the stronger concept of componentwise exponential asymptotic stability, which may be characterized in terms of nonlinear algebraic inequalities. Copyright (C) 2001 IFAC.