Some Types of Stability For Nonlinear Systems Using Generalized Lyapunov-Like Function

By using the definition of generalized Lyapunov –Like function and some types of stability , we give a new bounds for Lyapunov function , which is lead to getting some types of stability depending on some hypothesis which is depend on this function . we proved that those bounds and hypothesis on Lyapunov function satisfies the conditions where the using nonlinear systems will be stable ,also the type of stability of the system depends on those bounds and hypothesis . We got four types of stability which are (globally stable, globally asymptotically stable, exponentially stable and uniformly exponentially stable).