On the stabilization of decentralized overlapping control systems: Part II

This paper deals with stabilization of a broad class of interconnected systems with a constrained control structure. It is assumed that an information flow matrix for the interconnected system is given. This matrix specifies which outputs of the system are available for constructing any input signal of the system. The notion of quotient overlapping fixed mode (QOFM) is introduced, and it is shown that a system is stabilizable with respect to a given information flow matrix if and only if it does not have any QOFM in the closed right-half complex plane. Moreover, if the system is stabilizable, it is shown how the controller can be obtained. In addition, the method proposed in this paper identifies which components of the controller do not contribute to the stability, and can be either removed from the control system, or replaced by simple gains, as far as the stability is concerned. Finally, an in-depth illustrative example is presented to clarify the main results.