Complexity-reduced guaranteed cost control design for delayed uncertain symmetrically connected systems

Complexity reduced guaranteed cost control design problem is considered for a class of nonlinear symmetrically connected uncertain state-delayed systems. Nonlinear systems with identical nominal linear both subsystems and symmetric connections are supposed. Point time-delays and norm bounded parametric uncertainties are considered. A reduced-order guaranteed cost control problem is constructed first. The dimension of its state equals to the dimension of a subsystem in the original system. Then, a memoryless guaranteed cost dynamic output feedback controller is designed for the reduced problem using the LMI approach. It is proved that when this controller is implemented into each subsystem of the original system then such decentralized output controller is a guaranteed cost controller for the overall system.