Decentralized Assignability Measure And Eigenvalue Mobility Of Generalized Decentralized Control Systems

A decentralized fixed mode (DFM)is an eigenvalue, which is not affected by any linear time-invariant local feedback controllers. Therefore, for a plant with decentralized fixed modes, the closed-loop poles cannot be decentralized assigned arbitrarily. As a result, the computation of DFMs is very important. However, in some practical cases, the system parameters are only known to some limited accuracy. Some small parameter perturbations will make a DFM become an assignable mode. Even if the system matrix parameters are fixed, can the system modes, being very close to a DFM, be altered by decentralized feedback control as required specifically? Obviously, it is not completely satisfactory if only a "yes/no" answer can be provided for the decentralized assignability of a system mode. Motivated by this, a continuous decentralized assignable measure is more useful than a discrete one.In this thesis, the decentralized assignable measure and the eigenvalue mobility are investigated for decentralized generalized state-space systems. Three new concepts, finite decentralized assignable measure, impulsive decentralized assignable measure and eigenvalue mobility, are introduced. The finite decentralized assignability measure is defined as the distance between a system and (systems which possesses a finite DFM at some ). The impulsive decentralized assignability measure of the plant is defined as the distance between its fast subsystem and the fast subsystem of (systems which possesses an impulsive DFM). The above measures reveal how close a mode is to become a DFM. The mobility of an generalized eigenvalue may be considered as the ratio of the neighbourhood to which it may be shifted with the controller gain used to effect such a change. The sufficient conditions of the decentralized assignable measure and the eigenvalue mobility are proposed and proved mathmatically. Detailed computing procedures are given. The obtained results are important to analyze the decentralized stabilization and stability for systems with small modeling perturbations. If a mode is very close to a DFM, its decentralized assignability measure and the eigenvalue mobility are both small. Thus large controller gains will be required in order to shift the system mode. The present work is a natural extension of that for the normal decentralized control systems. The extension is not trivial and is significant. Some numerical examples are given to illustrate the design procedures.