Uncertain Robust Control Of The Discrete-Time Systems With Time-Delay

This paper deals with the problem of robust control for the uncertain discrete-time systems with time-delay. The robust control of the discrete systems is a branch of the control theory. It is parallel with the continuous systems' theory. The discrete-time systems, especially with uncertain and time-delay exist in the fact with the spreading of the field for the study of the system's theory and the applying of the computer's technology. The main works of the paper are study of the robust stability condition and the method of robust controller design. It is as follows.Fist, the problem of robust stability for the uncertain linear discrete-time systems is studied where the uncertain matrixes are unstructured , highly structured, norm bounded and matrix polytope structured . The relevant conditions that the systems is robust stability are obtained using the characteristic value method, Lyapunov function method and linear matrix inequality method. Then we give some examples to prove.Second, the problem of robust stability for the nonlear uncertain discrete-time systems is studied. The conditions of robust stability are presented using Lyapunov function method, and the collect of the matrix for the Lyapunov equation is studied. Third, the problem of robust stability for the uncertain discrete-time systems with time-delay is studied. For uncertain linear time-delay systems with highly structured, the conditions of delay-dependent robust stability are obtained using the characteristic root method. Fourth, the problem of robust controller design for time-delay systems is discussed. For linear uncertain time-delay systems with norm bounded, the state feedback controller is designed by Lyapunov method. And the state feedback controller based on the solution of a LMI, then an example is given to prove .At the same time, for linear uncertain time-delay systems with unstructured and highly structured , the conditions of robust stability are presented based on the system's solution. The method of the controller design is given using the approach of poleassignment.