Decentralized linear–quadratic control and stabilization for networked control systems with d-step delay

This technical communique studies decentralized state feedback control and stabilization for networked control systems with time delay. Unlike previous studies with conservative conditions — such as lower block triangular systems, uncorrelated process noises, and classical information structures — we investigate a more general coupled system with a non-classical d-step delayed state sharing pattern and correlated process noises. The main challenge lies in that variable measurability of controllers caused by time delay complicates solving forward–backward stochastic difference equations which can be addressed using linear controller forms and the projection theorem. The key contributions are: (1) deriving an explicit form of the optimal linear controllers via Riccati equations, and (2) providing a sufficient condition for mean-square boundedness. A dual-motor drive system is used to validate the theoretical results.