Decentralized Prescribed-Time Output-Feedback Control for Interconnected Systems with Coupled Non-Identical Subsystems of Different Orders

The challenge of decentralized control arises from the necessity to use only local information for constructing feedback mechanisms, with the goal of suppressing interactions among subsystems while ensuring the overall stability and performance of the entire system. The problem is significantly complicated when interconnected subsystems possess non-identical nonlinear dynamics with arbitrary relative degrees. We propose a novel time-varying decentralized control architecture that achieves global prescribed-time stabilization for the overall system through local output feedback. The developed scheme guarantees convergence to the equilibrium within any user-defined time interval, with temporal performance decoupled from initial conditions and independent of other controller parameter selection. Firstly, the decentralized prescribed-time observers for subsystems are systematically constructed to reconstruct full-state information, forming the basis for output-feedback synthesis. Secondly, a decentralized matrix pencil framework is established by incorporating symmetric positive-definite solutions of parametric Lyapunov equations, enabling concurrent management of intrasubsystem state/observer error dynamics and inter-subsystem couplings. This strategy facilitates the derivation of low-conservative design parameters while enhancing the applicability of the control algorithm. Finally, our findings demonstrate that the proposed approach is capable of accommodating a general system model characterized by unknown interaction strengths and arbitrary relative degrees. The theoretical results are validated through two simulation examples, confirming the effectiveness of the developed control scheme.