Association Delay Dependent Decentralized H_ ¡Þ Control Theory And Applications

The decentralized control for interconnected large-scale systems is widely used in practical applications. Time delay happens in many practical systems. The existence of time delay is the root cause of systems' unsatisfying performance. Delay is divided into delay independent and delay dependent. Delay independent results are rather more conservative, and the delay dependent results are flexible. The time delay conditions for the decentralized controllers are nonlinear matrix inequalities, which are very difficult to solve. Moreover, the results of decentralized controller design for the interconnected large-scale systems with time delay are often more conservative. This paper studied the large-scale interconnected systems delay dependent decentralized H_∞control theory and its applications. The main contents of this paper are shown as follows:(1) Constant delay dependent decentralized H_∞controller for a class of uncertain interconnected systems is considered. By combining the Lyapunov-Krasovskii functional approach, the delay integral inequality of matrices and variable substitution, the delay dependent sufficient conditions of small conservative for the existence of robust decentralized H_∞control are obtained in terms of linear matrix inequalities. The numerical simulation shows the validity of the main results.(2) Delay dependent decentralized robust H_∞controller for a class of interconnected systems is considered. The time delays are assumed as time-varying. The decentralized state feedback and output feedback H_∞controllers are designed. A method called integral inequality method is introduced. By combining the Lyapunov-Krasovskii functional approach, the delay dependent sufficient conditions of small conservative for the existence of robust decentralized H_∞control are presented in terms of nonlinear matrix inequalities. By using the modified cone complementary linearization algorithm, the controller design methods of LMI and the iterative algorithm are obtained. Results show that by using the designed control strategy which has less conservative, the stable range of time delay interconnected systems is expanded.(3) According to three-machine power systems, the model of two delay dependent power subsystems are made. The interconnected decentralized output feedback H_∞controllers are designed for constant delay and varying delay power systems. Using the controller, the stable and H_∞control problems of the power systems are discussed. The response curves of the interconnected delay three power systems are made, and the results show that the designed controller can improve the power system stability effectively and has good dynamic responses.