Robust Decentralized Control for Uncertain Interconnected Delayed Systems using Reduction Method

The stabilizing problem for interconnected delayed systems with parametric uncertainties was studied. The design procedure of robust decentralized controllers was the so-called reduction method which was used for the delayed systems with different known constant delays in inputs and interconnections. The delayed systems were reduced by defining a linear state transformation. Then employing a new Lyapunov function, a sufficient condition for the existence of the robust decentralized controllers is derived in terms of linear matrix inequalities (LMIs). And a parametrized characterization for a set of decentralized controllers (if they exist) is provided. Finally, a numerical example is given to illustrate the proposed method