Robust decentralized H∞ control for uncertain discrete time-delay systems: LMI approach

This paper considers a robust decentralized H_∞ control problem for uncertain multi-channel discrete time-delay systems. The uncertainties are assumed to be value-bounded, and exist in the system, time-delay and output matrices. Our interest is focused on dynamic output feedback. A sufficient condition for the uncertain multi-channel discrete time-delay system to be robustly stabilizable with a specified disturbance attenuation level is derived based on the theorem of Lyapunov stability theory. By setting the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller, which is reduced to a feasibility problem of a linear matrix inequality (LMI).