Decentralized Generalized H2 Control of Multi-Channel Uncertain Systems with Time-Delays

This paper considers a decentralized generalized H₂ control problem for uncertain multi-channel systems with time-delays. 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 uncertain multi-channel time-delay system to be admissible 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, the problem is reduced to linear matrix inequalities which are sufficient to the existence condition but much more tractable. An example is given to show the efficiency of this method.