A Characterization of approximate decentralized fixed modes of time-delay systems

The concept of decentralized fixed mode (DFM) is crucial in determining the output feedback stabilizability by linear time-invariant (LTI) decentralized controllers. However, in some cases, although a system has no DFMs, some of its modes may be very close to being fixed. It is thus important to characterize these modes, which are called approximate DFMs (ADFMs). In this paper, the characterization of ADFMs is discussed for LTI neutral (possibly descriptor-type) time-delay systems under static and dynamic decentralized output feedback control laws, and a mode mobility measure is proposed to provide quantitative information about ADFMs. To analytically compare the proposed measure, some of the commonly used quantitative measures for the characterization of ADFMs of finite-dimensional systems have also been extended to the considered type of systems. The herein proposed approach allows multiple time delays and does not require additional expansions or preliminaries for multi-input multi-output systems, like some other commonly used methods. Thus, characterization with this measure, in general, requires less computational load, while it can provide more explicit information about the controller effort than the other considered measures.