If we then design line control for this extended system such that will make it

asymptotically stable with prescribed dynamics according to the reference model, this will automatically fulfil the desired control goal in steady state, as well as in very good quality in transient states.

In order to show that the zero solution is globally

asymptotically stable, we will have to require an additional condition.

The necessary and sufficient condition for the controlled delayed species model (11) to be

asymptotically stable at fixed point is r - 1 > 0, 2[k.

Then the system is uniformly

asymptotically stable at equilibrium point x = 0.

We analyze the stability of the model both with and without treatment and derive sufficient conditions on treatment to ensure a globally

asymptotically stable cure state.

The fractional-order time-delay system (33) is

asymptotically stable, if there exist symmetric positive definite matrices P and Q, such that the following LMI is feasible:

Secondly, a state feedback controller is designed which guarantees that the resulting closed-loop system is

asymptotically stable and possess a prescribed H [?

Conditions of the existence of the disease free and endemic equilibrium point are derived and proved that the disease free equilibrium point is locally

asymptotically stable under the given parameters.

The necessary and sufficient conditions for this system to be

asymptotically stable, that is, a system where all the movements flow cyclically or non-cyclically towards a stationary equilibrium point, are that the [OMEGA] Jacobian matrix trace be negative and its determinant positive.

Theorem 2 can be derived from the above analysis: if suppose assumption 1) and 2) set up, then nonlinear neural network (6) exists the only balance point which is globally

asymptotically stable.

Using the IML, it is possible prove that y = 0 is

asymptotically stable if and only if R([lambda]) < 0 for any eigenvalue [lambda] of the matrix Df([bar.

In this context, the objectives of this paper are to determine two limits for the nonlinear gain of the error-squared controller, so that a closed-loop system with such controller is

asymptotically stable in the Lyapunov sense and to realize a performance analysis.