Robust decentralized H∞ control for multi-channel discrete-time systems

This paper considers a robust decentralized H_infin control problem for uncertain multi-channel discrete-time systems with time-delay. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in the system, time-delay and output matrices. Our interest is focused on dynamic output feedback. A sufficient condition for the multi-channel uncertain discrete time-delay system to be robustly stabilizable with a specified disturbance attentation 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). An example is given to show the efficiency of this method.