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1. It is discovered that convergence rate with asymptotical optimality for the proposed EB test can arbitrarily approach to 1 under certain conditions.

2. The problem of asymptotical stabilization for a class of uncertain systems with sector nonlinear input is discussed.

3. We proved the closed systems global asymptotical stable, not needing the error upper bound and the error square integral, all the signals are bounded and the tracing error convergence.

4. The asymptotical behaviors and periodic oscillations have been studied by applying the modern theories of difference equations.

5. The stability of the closed-loop system's and its asymptotical convergence of tracking errors can be guaranteed.

6. Based on range-partition, this paper proposes an efficient asymptotical algorithm of load balance to insure the storage balance in any time(sentence dictionary), and demonstrates its validity through theory analysis.

7. It is proved that globally asymptotical stability and convergence of the resulting closed-loop system are guaranteed by the range of the prediction horizon.

8. Finally, the asymptotical distribution of the smoothing estimator related to the extended moment estimator is derived by the study of process before.

9. Through analysing the local uniform asymptotical stability at origin under the proposed point stabilization control law, the scale of control parameters is confirmed.

10. First we obtain well posedness and show that strongly asymptotical stability of closed loop system by using the method of linear operators semigroup.

11. Consequently the goal of robust tracking control was obtained and the asymptotical stability of adaptive sliding mode control systems was proved based on Lyapunov theory.

12. If R 01 , a unique endemic equilibrium is locally asymptotical stable under a special condition.

13. A type of structure self organizing algorithm is presented to guarantee close loop asymptotical stability.

14. By computing the spectral radius of matrix exponent, it is very easy to evaluate the asymptotical stabilization.

15. In other words, the unstable limit cycle will be bifurcated from the original asymptotical stable equilibrium point at another higher series compensation level, and the system dynamics will change.

16. This research indicates that state feedback controller without delay can be chosen to guarantee the robust global uniformly asymptotical stability of integro-differential systems.

17. In this paper , some sufficient conditions of global asymptotical stability of the zero solution are given.

18. By the above facts, it is necessary in analyzing globally asymptotical stability of the origin that the other asymptotical stability equilibrium points are false ones.

19. The decentralized state feedback controllers are designed using linear matrix inequalities (LMI) such that the well working order descriptor systems are asymptotical stabilization.

20. Besides, an adaptive controller with projection algorithm as parameter estimation law is designed for the slow subsystem control and its asymptotical stability is proved.

21. In order to apply well to the process with time delay, a model-free predictive control law for the PSD is proposed which scheme is based on the asymptotical stability in delay-free PSD system.