GENERALIZATION OF LA SALLE'S THEOREM

1 IntroductionIn the study of absolute stability for Lurie control system. The importantcontribution of La Salle's Theorem is to reduce the number of the conditions onthe control parameters. In 1966, famous mathematician LefSchetz has pointedthe importance of the La Salle's result. In papers 1,3], the authors discussedthe absolute stability of the following systemhere A is an n x n constant matrix, 5 and c are constant n-dimensional vectors(which are non--zero), p is a positive constant, …

GENERALIZATION OF LA SALLE'S THEOREM

In this paper, by using the method of Lyapunov function we generalize the theorem of La Salle from Lurie control system to general Lurie control system. Our result is concise and is easy to be tested. Hence, we improve the proof and extend the applied range of La Salle's Theorem.