STABILITY OF NONLINEAR SYSTEMS THROUGH ENERGY - LIKE LIAPUNOV FUNCTIONS

Abstract

The results derived in earlier works on the stability of linear vector equation of the type, St + H± Gx = 0, which were obtained through the use of energy-like Liapunov functions, are extended in this paper to nonlinear and time varying vector equations of the type, I + h(z,x,A) + g(t,x) = 0. The derived results are useful only for certain types of g (t, x). Stability analysis of a discretized partial differential equation through the method described can help in choosing a suitable Liapunov functional for the original equation.