1989 Volume 25 Issue 3 Pages 304-310
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.
