On the stabilization of decentralized overlapping control systems: Part I

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 an interconnected control system is given, which represents 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 on the complex plane, by using 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, the design procedure for obtaining a stabilizing controller for the systems with no unstable DOFM is presented. In addition, the problem of optimal LTI structurally constrained controller with respect to a quadratic performance index is discussed. The numerical examples given, demonstrate the effectiveness of the proposed method. In part II of the paper, the necessary and sufficient conditions for the existence of a non-LTI stabilizing structurally constrained controller are given, when no LTI controller can stabilize the system.