Cooperative $\mathcal{H}_\infty$ Fault-Tolerant Tracking with ISS Guarantees for Networked Systems with Sensor Faults

Abstract

This paper develops a cooperative fault-tolerant tracking framework for heterogeneous networked linear systems subject to sensor faults and external disturbances. Each unit employs an augmented $\mathcal{H}_\infty$ observer that jointly reconstructs the system state and unknown sensor fault, providing disturbance-attenuated estimation guarantees. An inner state-feedback gain is synthesized through convex $\mathcal{H}_\infty$ Linear Matrix Inequalities (LMIs) to ensure robust closed-loop stabilization and disturbance rejection, while an outer distributed integral action eliminates steady-state tracking offsets and enables cooperative tracking of a setpoint source. The resulting cooperative error dynamics are shown to satisfy an Input-to-State Stability (ISS) property with respect to disturbances and residual estimation uncertainty, and converge exponentially to zero in the disturbance-free case. Furthermore, vanishing cooperative error guarantees network-wide consensus tracking of the desired setpoint. Numerical studies on heterogeneous DC-motor networks with star, cyclic, and path communication topologies demonstrate accurate state and fault estimation, robust cooperative tracking, and resilience against disturbances and time-varying sensor faults. The proposed framework provides a scalable and robust coordination strategy for interconnected systems operating under sensing imperfections and uncertain environments.