Enhancing System Resilience Through Decentralized Control Loops: Separating Bounded Fault Tolerance from Network-Level Resilience

Table 1. Structural conditions for resilience in decentralized control. Each conditionis valid only for the disturbance model against which it was derived.

Property	Disturbance model	Structural condition	Verification evidence	Key sources
Bounded fault tolerance	Isolated loop outage	Steady-state gain condition	Gain matrix / passivity / sector-bound test	Grosdidier and Morari (1986); Campo and Morari (1994); Zhang et al. (2002); Bao et al. (2003)
Consensus under silent node	Node or link goes silent	Graph connectivity	Communication graph remains connected	Simpson-Porco et al. (2015); Bidram et al. (2013, 2014)
Consensus under compromise	Up to F compromised nodes	2F+1 neighbors per normal node	Neighbor-redundancy verification	LeBlanc et al. (2013)
Distributed optimization under faults	Bounded faulty or adversarial agents	Minimum redundancy condition	Redundancy characterization	Gupta and Vaidya (2020)
Networked control stability	Network-induced delay	Delay margin	Delay threshold relative to process dynamics	Hespanha et al. (2007)
Distributed MPC	Inter-controller exchange delay	Sampling-interval completion	Timing verification	Christofides et al. (2013)