Norm Continuity And Robustness With Respect To Small Delays For Exponential Stability Of Two Classes Of Delay Systems

Norm continuity and robustness of stability with respect to small delays in the control theory are challenging and heated topics, from the point of view of theory and application .At the same time, it is very likely that time delays will occur in our everyday life. Therefore, it is an important mathematical and system theoretical value to study the norm continuity and robustness of stability with respect to small delays. In this thesis, we mainly concentrate on the following problems:1. Norm continuity of the Pritchard-Salamon systems with delay;2. Norm continuity and robustness of a class of abstract semi-linear functional differential equations with respect to small delays.In order to solve the above-mentioned, the following aspects need to be taken into accont. Above all, we study the norm continuity of the solution semigroup corresponding to the Pritchard-Salamon systems with delay in the two phase spaces .This property is considered as the combination of the perturbation and delay. However, we can see no literatures on such property about this aspect. Thus it is a flash-point. Furthermore, we discuss the norm continuity of the semi-linear functional differential equations with respect to small delays in the continuous space. In the end, the robust stability of this system with respect to small delays is proved without the exponential stability of the initial semigroup in the same space. So it is a new programe to be compared with the present literatures.