As is well known, for each proper transfer matrix of the linear time-invariant system, there exist coprime factorizations over
RH∞, and these can be used to construct the set of all proper real-rational controllers stabilizing the plant. By choosing controllers from the set, we can solve the problem of robust control and the problem of
H∞ optimal control. For decentralized linear time-invariant control systems, it is also necessary to look for the set of all proper real-rational decentralized controllers so as to solve the problem of the decentralized robust control and that of the decentralized
H∞ optimal control. The stable factorization of the plant's transfer function matrix for the decentralized controllers can take a special form which we call decentralized coprime (d-coprime) factorization. This paper shows that the set of decentralized controllers that stabilize the plant can be found by using the unimodular matrices which keep up the property of d-coprime factorization. The problems of robust and
H∞ optimal control for decentralized systems are provided with the same form as that of the problem of general systems, except for the numbers of the free parameters.
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