Decentralized Finite‐time Control for a Class of Large‐scale Systems with Symmetrically Interconnected Subsystems

The finite‐time stability (FTS) of a symmetrically interconnected system is studied under the consideration of utilizing the system structural properties to reduce the complexity of analysis. The FTS of this kind of large‐scale system can be guaranteed by that of two lower dimensional systems. The concept of mixed stability, taking care of both transient and steady‐state performances of a system, is introduced. Based on the FTS analysis, a decentralized finite‐time controller via state feedback is given to stabilize the large‐scale system. Meanwhile, an observer‐based decentralized output feedback controller is provided to make the closed‐loop system finite‐time stable. The FTS conditions and related decentralized stabilization controller parameters are both derived from solving some differential or algebraic linear matrix inequalities.