Robust Control For Uncertain Time-delay Systems

In the production practice, uncertainty is pervasive. The system robust control is to solve the uncertainty in practical production. Robust H? theory is an important branch of robust control theory that has a more complete theory system and that has achieved many remarkable achievements in many fields, so it attracted many scholars participate in the study. And apparently robust H? theory has become a very active research direction. On the other hand, Time-delay phenomenon also is universal in the natural and social conditions, such as nuclear reaction processes, steel rolling process, neural network and so on. The phenomenon of time delay that is also a hot issue in control area is one of the important factors to lead to instability of the systems, so it become more important for many more domestic and foreign scholars. Now many scholars combine the uncertainty with time-delay, and they have achieved important results.The robust control for uncertain time-delay systems is the subject of the paper. In this paper, on the basis of previous research works, according to lyapunov stability theory and linear matrix inequality method, we can gain system stability criterion and robust stabilization criterion. And numerical examples show good feasibility of the method in this paper.the method in this paper is mainly that, according to formula of Newton-Lebniz, We can do an equivalent transformation for the Equation of state of the system, then for the Equation of state x(t)=Ax(t)+Adx(t-d(t)), to do an equivalent transformation, we have x(t)=(A+Ad)x(t)+Ad?(t-d(t)x(s)ds, and then according to the new Equation of state, we could research robust control problem. In this paper, the main results are as follows:(1) A class of the stability of uncertain time-delay systems and the design of methods of state feedback controller. On the basis of the new equation of state, constructing a lyapunov function, and according to linear matrix Inequality method and free weighting matrices method, we can obtain the sufficient conditions of system stability. Compared with other methods which also use the free weighting matrices Method, the results' structure basing on the method in this paper is simple, and numerical examples show good feasibility of the method in this paper.(2) A class of robust H? control for uncertain time-delay systems. Based on the method mentioned previously, and In light of the performance index of the system, we can have the sufficient conditions of asymptotic robust stability and the design of robust H? control systems. Numerical examples are given to illustrate the effectiveness of the paper.