AN IMPROVED INVARIANCE-LIKE THEOREM

Stability theory plays a significant role in fault-tolerant controller designing and closed loop systems stability analysis. To use Lyapunov stability theorem, Lasalle invariance principle and some other invariance-like theorems, we should firstly construct a energy-like function V; V, the derivative of the function V, should be guaranteed to be nonpositive. When the sign of V is variable, an improved invariance-like theorem for a class of nonlinear nonautonomous systems is presented, and it is proved that the theorem 8.4 in (Khalil, 2002) is a special case of the proposed invariance-like theorem.