New Necessary and Sufficient Conditions for Decentralized H∞ Control of Discrete-time Interconnected Systems

This paper is concerned with the decentralized H-infinity control problem of discrete-time interconnected systems. The studied interconnected system is transformed equivalently into a single linear time invariant system with matrix inversion terms in the system matrices. This paper derives novel necessary and sufficient conditions such that the considered interconnected system is asymptotically stable with the prescribed H-infinity performance. The new conditions are computationally attractive because of the elimination of matrix inversion terms. Then these conditions are transformed into linear matrix inequalities. The decentralized controllers can be obtained by solving linear matrix inequalities to guarantee the stability and the H-infinity performance of the closed-loop interconnected system. Finally, the effectiveness and the advantages of the proposed results are demonstrated by one numerical example.