In this paper we study a method for constructing Lyapunov functions defined on the whole region of attraction of an exponentially stable equilibrium point of nonlinear autonomous systems. The method involves solving a partial differential equation. We prove that a solution exists in the region of attraction. When the eigenvalues of the linearization of the system are non-resonant, a power series solution can be found, and its region of convergence can be used to determine the region of attraction.
|Number of pages||5|
|Journal||Proceedings of the IEEE Conference on Decision and Control|
|State||Published - 1999|
|Event||The 38th IEEE Conference on Decision and Control (CDC) - Phoenix, AZ, USA|
Duration: Dec 7 1999 → Dec 10 1999