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

This letter is concerned with the decentralized <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 letter derives novel necessary and sufficient conditions such that the considered interconnected system is asymptotically stable with the prescribed <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance of the closed-loop interconnected system. Finally, the effectiveness and the advantages of the proposed results are demonstrated by one numerical example.

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