Decentralized control in the discrete-time systems with interconnected delays

This paper addresses the decentralized control problem of a class of discrete-time linear time-invariant (LTI) systems composed of two interconnected subsystems. By means of the well-known projection theorem, a suf.cient stability condition of such systems is established, which is less conservative than the existing results. This condition is then extended to the case where the systems involve delays. All the conditions can be veri.ed by a combination of linear matrix inequalities (LMI) toolbox and optimal search algorithm of Matlab. Numerical example is provided to illustrate the effectiveness and advantages of the obtained results.