A Necessary and Sufficient Condition for the Existence of a LTI Stabilizing Decentralized Overlapping Controller

This paper deals with the stability of the large-scale interconnected systems with a constrained control structure. It is assumed that the information flow matrix for the interconnected control system is given. This matrix determines which outputs of the system are available for constructing any input signal of the system. The notion of decentralized overlapping fixed mode (DOFM) is introduced, and it is shown that those modes of the system which are not DOFM, can be freely placed anywhere in the complex plane, by means of a linear time-invariant (LTI) structurally constrained controller. This implies that the system is stabilizable by a LTI structurally constrained controller, if and only if it does not have any unstable DOFM. Furthermore, a design procedure is proposed to obtain a stabilizing controller for the systems with no unstable DOFM. In addition, the problem of optimal LTI structurally constrained control design with respect to a quadratic performance index is discussed. The numerical examples given demonstrate the effectiveness of the proposed method