The Study On The Stability Of Linear Interval Systems With Time-Delay

In the study of control theory, the results on the stability of interval matrix system and time-delay system have made a progress. Now the stability of interval matrix system with time-delay, joining the interval matrix and time-delay system, has become more and more important in the control theory.A general method that firstly chooses a positive Lyapunov function with matrix invariant, then considers the derivative of that Lyapunov function on any time and guarantees the time derivative be positive can obtain the stability of interval matrix with time-delay. From the contents, ordinary methods on researching the stability of interval matrix with time-delay are considered, such as Lyapunov function method, constructing M-matrix method, matrix measure method, LMI method etc.In this paper, the theory and the development of the stability of time-delay system and interval matrix system are summarized firstly, and the system stability and LMI theory referred in the paper are stated.Then the stability of interval matrix with time-delay is discussed and the main results are given. By constructing the different Lyapunov functions, some different sufficient conditions are derived. In terms of LMI theory, another result also can be obtained. Additionally, some numeral examples are given to illustrate the exactitude of theories and the availability of method in this thesis. Finally, the author puts forward some thoughts on the stability of the interval matrix with time-delay.