On Structurally Constrained Control Design with a Prespecified Form

This paper deals with the decentralized overlapping control of interconnected systems. It is shown how the existing results aiming at designing a decentralized controller of a certain type such as static, dynamic, finite-dimensional linear time-varying, and sampled-data can be utilized to design a decentralized overlapping controller of a desired form, in order to achieve the design specifications. It is known that quotient fixed modes (QFM) of a decentralized control system are fixed with respect to any general (nonlinear and time-varying) decentralized control law. Generalization of this result to the decentralized overlapping control problem, i.e. the case when the control structure is only partially localized, is not trivial at all. The notion of quotient overlapping fixed mode (QOFM) is introduced and it is shown that a mode of the interconnected system can be shifted by means of a general decentralized overlapping controller if and only if it is not a QOFM. It is then asserted that any interconnected system with no unstable QOFM can be stabilized by using an appropriate finite-dimensional linear time-varying controller. This work takes advantage of the new developments in analysis and design of decentralized control systems. The efficacy of the results is elucidated through a numerical example.