Study On Robust Control For Linear Singular Systems With Time-Delay

It makes us impossible to get the precise model of controlled objects in most practical engineering applications, due to the existence of uncertainties caused by the measurement parameter-error, the changing of running condition, etc. To study on robust control for singular systems, is to research how to design a control law to stabilize the resultant closed-loop system and keep some dynamic performances when satisfied a range of parameter uncertainties. Therefore, the study on singular systems is significant both in theory and in practice, because singular systems have more widespread form compared with regular ones.The robust control for linear singular systems with time-delay is studied on the basis of Lyapunov function and linear matrix inequality(LMI) in this dissertation, including the robust stability of uncertain continuous-time singular systems and uncertain discrete-time singular systems with time delays. The main contents of this dissertation are outlined as follows.1. A sufficient condition of robust stability with LMI form is presented according to nominal continuous-time singular systems with time-varying delays, by selecting the proper Lyapunov function, and the condition is delay-independent. Then the conclusion is extended to the uncertain case. It is worth nothing that the condition has no limitation requirements on the time-delay d(t), and numerical examples show the effectiveness of the conclusion.2. A new sufficient condition of robust stability with LMI form is presented at first according to nominal discrete-time singular systems with time-varying delays when the varying time-delay is bounded. Then the conclusion is extended to the case of uncertain condition, and numerical examples show the effectiveness.