Title :
Stability regions of nonlinear autonomous dynamical systems
Author :
Chiang, H.-D. ; Hirsch, Morris W. ; Wu, Felix F.
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA
Abstract :
A topological and dynamical characterization of the stability boundaries for a fairly large class of nonlinear autonomous dynamic systems is presented. The stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points (and/or closed orbits) on the stability boundary. Several necessary and sufficient conditions are derived to determine whether a given equilibrium point (or closed orbit) is on the stability boundary. A method for finding the stability region on the basis of these results is proposed. The method, when feasible, will find the exact stability region, rather than a subset of it as in the Lyapunov theory approach. Several examples are given to illustrate the theoretical prediction.<>
Keywords :
nonlinear control systems; stability; topology; autonomous systems; dynamic systems; nonlinear control systems; stability boundaries; stability region; topological characterisation; Economic forecasting; Environmental factors; Laboratories; Lyapunov method; Orbits; Power generation economics; Power system economics; Power system stability; Sufficient conditions;
Journal_Title :
Automatic Control, IEEE Transactions on
