Properties of Nonlinear System (Related to Theorem)
November 26, 2008 2 Comments
Theorem 1.1 (Local Existence and Uniqueness)
With the presumption that f from ;Vis continuous on t and x, and finite constant h, r, k and T exist, so that:
where is a ball in of the form:
then ;V has just one solution in the interval where the number is sufficiently small to satisfy the inequalities:
for some constant
Theorem 1.2 (Global Existence and Uniqueness)
Suppose that for each there exist finite constant and such that
Then ;V has only one solution in the interval .
;V is taken from Definition 1.6 (System’s Trajectory-Solution)
Vukic, Zoran, Kuljaca, Ljubomir, Donlagic, Dali, Tesnjak, Sejid, Nonlinear Control Systems, Control Engineering Series, Marcel Dekker, New York USA, 2003.