Some new results on the stabilization and state estimation in large-scale systems by decentralized and multilevel schemes.

The main objectives of this dissertation are the following. The first objective is concerned with the stabilization of large-scale systems by a decentralized control. The fundamental idea behind this type of control is the stabilization of the isolated subsystems of a large-scale system in such a way that the global stability requirement is also satisfied. For this purpose, a new stability criterion is introduced to identify a class of interconnected systems that can be stabilized by local state feedback. In addition to this, two specific classes of interconnections are presented for which the overall system stability can be ensured by a decentralized approach. A new constructive procedure for the design of decentralized controllers for the identified classes of large-scale systems is discussed. The principal advantages of this design procedure are that it requires a minimal amount of computation and is a systematic procedure eliminating the trial and error arguments as in the earlier methods. The second objective of the dissertation is to investigate the problem of the stabilization of a class of large-scale systems which are composed of identical subsystems and identical interconnections. For this class of systems, certain significant theorems, concerning the qualitative properties are introduced. Following the guidelines set forth by the above theorems, a few different schemes for the decentralized and multilevel control of the aforementioned class of large-scale interconnected systems are presented. The third objective concerns the development of a few different schemes for the design of an asymptotic state estimator for large-scale systems described as interconnections of several low-order subsystems. The most attractive feature of the present schemes is that the majority of the necessary computations are performed at the subsystem level only, thereby leading to a simple and practicable estimator design. Finally, all the above results are illustrated by numerical examples. Further, a comparison study is conducted to show the advantages of the methods and the results in this dissertation in comparison with some results available in the literature