Stabilization of dynamical systems is a very important problem and has received great attention. The solution of such problems can be achieved for linear autonomous small scale (centralized) systems with specific parameters using the conventional control theory. This leads to the design of a centralized controller which determines the control actions based on the centralized structure. However, with the development of modern technology, the size and complexity of the systems are increasing everyday, stabilization of large scale systems using centralized techniques is therefore not feasible. And decentralized techniques are an attractive approach for large scale systems stabilization. Our objective in this research is to investigate the stability of linear nonautonomous large scale systems with uncertain parameters. Both feedback-free and feedback control systems will be studied. The technique is based upon using a Lyapunov function to disconnect and reassemble the subsystems in different ranges. So new criteria for studying and designing the finite-time or uniform stability can be developed. These criteria can also be used to design or estimate the convergence rate of the global system. In addition, since small scale (centralized) systems. Examples are given. Application and extensions are also discussed.
The Richmond Group (Late Ordovician) in the tristate region of southwestern Ohio, north-central Kentucky, and southeastern Indiana consists of a succession of clastic and carbonate sediments deposited on a prograding intracratonic ramp and distal clastic fan. Six regional depositional facies have been delineated during a detailed examination of cores, outcrops, and geophysical logs across a 325 by 350 km study area. The facies, informally designated Facies A through F, are assigned to depositional environments consisting of: a shale-dominated shale distal intracratonic ramp; mixed carbonate and shale proximal intracratonic ramp; shallow subtidal to supratidal intracratonic ramp, and shallow-water, distal clastic wedge; based on their sedimentologic and paleontologic characteristics. Regional cross sections of these facies indicate that the distal clastic wedge prograded from the east and that the intracratonic ramp prograded from the south. In addition, isopach maps indicate that the depocenter of the basin was located southeastern Indiana and southwestern Ohio.