Guaranteed Cost Control For Uncertain Singular Time-Delay System

The guaranteed cost control problem was proposed in the early 1970s. The basal idea is to design a state feedback control law such that the closed-loop systems are stable, while the cost index of the closed-loop systems is within a certain bound for all these admissible uncertainties. Also, uncertainty and time delay are commonly encountered in a variety of engineering systems, Such as telecommunication systems, electrical network, chemical processes and so on. The existence of uncertainty and time delay in a dynamical system may induce instability or poor performances. On the other hand, singular systems contain many uncertain singular systems with time delay, which are the more general form systems with abroad applied background than normal systems. Therefore, the investigation of guaranteed cost control for uncertain singular systems is important both in theory and practice.The main results obtained in this dissertation are as follows:(1) In terms of linear matrix inequality approach, the problem of guaranteed cost control is discussed for singular time-delay systems with norm-bounded parameter uncertainties. A delay-dependent condition of the state feedback guaranteed cost controller is proposed adopting directly new quadratic term integral inequality without model transformation, and also the controller design method is provided.(2) The delay-dependent guaranteed cost controller satisfies H_∞disturbance problem is studied for a class of singular time-delay systems with norm-bounded parameter uncertainties. The optimal guaranteed cost index and optimal H_∞disturbance attenuation level are derived and the H_∞controller design is also given via linear matrix inequality technique.(3) The problem of delay-dependent guaranteed cost resiliently control is considered for a class of singular time-delay systems with norm-bounded parameter uncertainties. The controller disturbance is assumed in a select range. Base on the linear matrix inequality technique, the delay-dependent sufficient condition for the existence of guaranteed cost controller is given, and the controller design method is also derived.