Research On Some Issues For Decentralized Connective Stabilization Of Large-scale Descriptor Systems With Expanding Construction

Decentralized connective stabilization problem of large-scale descriptor Interconnected systems with expanding construction has attracted attention from many scholars. Due to the particularity of the descriptor systems, it is more complex than the normal systems to design controller and analyze stability. Besides stability of the systems, the regularity and impulse immunity must be considered for the descriptor systems. The structural change or reconstruction of the system has a great influence on the stability. In order to reduce it, four relevant problems in terms of structural connective stability control of large-scale descriptor systems are studied in this paper. Specific contents are as follows:1. Robust decentralized connective stabilization problem for large-scale descriptor interconnected systems with structural reconstruction is studied by using Lyapunov theory and LMI approach. Mainly aimed at two cases of the structure reconstruction, one is subsystem may be disconnected and then reconnected, the other is considering the structure of extension, namely some new subsystems are added to an original structure. For both cases connective stable problems are studied, Then, the sufficient conditions of robust decentralized connective stabilization is obtained for large-scale descriptor systems with expanding construction,and design approach of the state feedback controllers is presented. Finally, a numerical example is given to show the effectiveness of the proposed approach.2. Robust decentralized connective stabilization problem based on descriptor dynamic output feedback is studied for a class of descriptor large-scale systems with expanding construction. The mathematical description of a class of descriptor large-scale systems with expanding construction is given and the sufficient conditions of robust decentralized connective stabilization is obtained for the descriptor large-scale system with expanding construction by using Lyapunov theory and LMI approach. And design two approaches of the connective stable controllers of descriptor large-scale systems with expanding construction. Finally, a numerical example is given to show the effectiveness of the proposed approach.3. Robust decentralized finite-time connective stabilization problem for a class of large-scale descriptor systems with expanding construction is studied. The concept is introduced of finite-time stability and connective stable to the descriptor large-scale systems with expanding construction in the design of decentralized control. The problem is to design the robust decentralized control law of the newly added subsystem on the basis of not changing the decentralized control laws of the original construction, so that the new subsystem and the expanded large scale system can keep finite-time connective stability. Based on state feedback and dynamic output feedback, the approach of the decentralized finite-time connective stabilization for this kind of systems is given by using LMI method. Finally, a numerical example is given to show the effectiveness of the proposed approach.4. Robust decentralized H-infinity control problem base on state feedback for a class of state time-delay large-scale descriptor systems with expanding construction is studied. The mathematical description of large-scale descriptor time-delay systems is given and the sufficient conditions of robust decentralized connective stabilization is obtained for the descriptor large-scale system with expanding construction by using Lyapunov theory and LMI approach. And design approach of the state feedback controllers is presented, as well as satisfying H-infinity properties. Finally, a numerical example is given to show the effectiveness of the proposed approach.