The decentralized control of large-scale descriptor systems

In this thesis, the problems of decentralized stabilization and regulation for general proper systems and descriptor systems are studied. A general proper system is one with general input feed-through, whereas a descriptor system is characterized by the existence of algebraic constraints on the plant state variables. It is shown that both systems are intimately related by a novel concept called "impulsive modes", and that the analysis of general proper systems is a prerequisite to that of descriptor systems. In both cases, the decentralized stabilization and regulation problem differ from conventional state space models. In particular, the direct feed-through term plays an important role in both types of systems and conditions are found to determine if a given general proper system/descriptor system can be stabilized (the decentralized pole-assignment problem) or/and asymptotically regulated (the robust servomechanism problem). Furthermore, conditions are provided to determine if a given descriptor system can be made impulse-free.; Related to the decentralized stabilization and regulation problems is the issue of robustness. Properties of decentralized descriptor systems subject to multivariable gain and time lag perturbation are studied. A special yet important case of gain perturbation is the case of sensor/actuator failure which leads to the reliable control problem. Conditions are obtained to determine if a solution exists to the reliable control problem and to provide an appropriate synthesis procedure.; Implementational efficiency requires a simple control structure with a minimum number of communication paths between the plant's inputs and outputs. The problem of minimal sensor/actuator placement is analyzed in Chapter 6 where existence conditions for a (possibly non-unique) minimal control structure and a controller synthesis procedure are obtained. A set of interaction indices is devised to assist in the controller synthesis for such a structure and to determine if a particular input/output pairing and synthesis sequence are feasible. In such studies, the plant is not necessarily assumed to be known.; Finally, for plants with given models, a parameter optimization method is applied to synthesize servo-controllers that exhibit "desirable" closed loop properties. Such procedures are described in Chapter 8.