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In the past three decades, the problem of decentralized control has been thoroughly investigated in the literature, and a variety of its aspects are studied [1, 2, 3]. More recently, the problem of decentralized overlapping control has attracted several researchers [4, 5].The decentralized overlapping control is fundamentally used in two cases: i) when the subsystems of a system (referred to as overlapping subsystems) share some states [6, 7, 8]. In this case, it is usually desired that the structure of the controller matches the overlapping structure of the system [8]; ii) when there are some limitations on the availability of the states. In this case, only certain outputs of the system are available for constructing each control signal.

In this work, we show how the double-Youla parameterization can be used to recast the robust tuning of a feedback controller as a robust estimation problem. The formulation as an estimation problem allows tuning of the controller in realtime on the basis of closed loop data. Furthermore, robust estimation is obtained by constraining the parameter estimates so that feedback stability will be maintained during controller tuning in the presence of plant uncertainty. The combination of real-time tuning and guaranteed stability robustness opens the possibility to perform Robust Estimation for Automatic Controller Tuning (REACT) to slowly varying disturbance spectra. The procedure is illustrated via the application of narrow-band disturbance rejection in the active noise control of cooling fans.

It is assumed in this book that, any time non-real eigenvalues and eigenvectors are assigned, the corresponding complex conjugate eigenval­ues and eigenvectors are also assigned. It is also assumed that assigned eigenvalues are never repeated.

In this Chapter, we do not intend to present new algorithms for model reduction but to throw some light on the mathematics behind projection techniques which are currently used for that purpose. In this respect, what follows can be considered as a continuation of [14, 15, 17] and the literature quoted in these papers.