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.