1. It can guarantee the global boundness of closed loop signals and make the output tracking error arbitrarily small.

2. The present paper deals with the uniform boundness and the ended uniform boundness of solutions for a nonlinear functional differential equation by using Lyapunov method.

3. Due to varying degrees of osmotic and matrix interactions, water activity describes the continuum of energy states of the water in a system rather than a static "boundness".

4. Som criteria on the asymptotic behavior (such as boundness, tending to zero) of solutions for a kind of third order delay functional differential equation are established.

5. When applied, they can ensure the global boundness of all closed-loop signals, and can make, the outputs of closed-loop systems sufficiently reach zero.

6. On the one hand, these estimates indicate the boundness of solutions to the problem in different functional spaces when the nonlinear terms satisfy some special conditions.

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7. The controllers are robust to some nonlinear uncertainties and bounded disturbance, and can ensure the global boundness of all closed loop signals.

8. All signals and states of the controller systems are ensured with global boundness , the tracking error converging to a residual set.

9. This paper discusses initial boundary value problem (1)-(3). Under somewhat more general condition, the uniform boundness of the solutions is demonstrated and the decay estimate is obtained.

10. The simulation result shows that the controller is robust to some nonlinear uncertainties and bounded disturbance, and it can guarantee the global boundness of all closed-loop signals.

11. The authors present two retarded versions of integral inequality, which can be used to ensure the boundness of solution to certain integral equation with time delay.