The essential characteristics of large systems is their high dimensionality due to which conventional control techniques fail to give reasonable solutions with reasonable computational efforts. A number of large systems encountered in practice are composed of subsystems with similar dynamics interconnected in a symmetrical fashion. The analysis and control of a large system with these particular features must take advantage of the existing structural properties to achieve computational simplifications of the overall problem. The focus of this thesis is the feedback design and analysis of large systems possessing the property of spatial symmetry. Specifically, the problems of controller design and analysis for infinite dimensional toeplitz systems and their finite dimensional analogs, circulant systems, are studied. These spatially symmetric systems are special classes of large systems. The first part of this thesis is focused on the development of formal controller design methodologies which take advantage of the properties of the circulant matrices. The key to this development is the use of the FFT algorithm to diagonalize circulant matrices. The resulting controller design methodologies are computationally attractive and easily applicable to large systems with circulant symmetry. More specifically, the H$\sb2$ and H$\sb{\infty}$ controller synthesis problems are studied in detail and are shown to decompose into lower order independent problems. The second part of this work concentrates on proving that certain finite order toeplitz systems are asymptotically equivalent in an appropriate sense to circulant systems. This result justifies the use of circulant control design techniques for certain toeplitz systems. Moreover, the closed loop effects of controlling a toeplitz system with a controller designed for its asymptotically equivalent circulant system are analyzed. The application of the developed theoretical results to a realistic example is the focus of the last part of the thesis. The adaptive optics system used in this example is modeled by a transfer function matrix with toeplitz symmetry. The computational efficiency of the controller design methodologies developed in this thesis is illustrated by designing a series of controllers for this system.

Aperture synthesis is applied to passive microwave remote sensing of the earth in an effort to attain high resolution images at low microwave frequencies. An L-band (1.4 GHz) synthetic aperture radiometer, dubbed the Electronically Scanned Thinned Array Radiometer, is tested and calibrated. The instrument is modeled after radio telescopes, and utilizes a thinned array of correlation interferometers to measure the Fourier Transform of the Brightness temperature image. The antenna hardware of such an array is reduced by comparison with real aperture antenna systems, which renders this technique relevant to future spaceborne remote sensing applications that require high resolution. In particular, it is the scientific applications at L-band, including the spaceborne remote sensing of soil moisture and ocean salinity, which have motivated this research. Aperture synthesis concepts are developed and applied to the theoretical ESTAR system in chapter II. Chapter II also includes a description of the prototype which was designed constructed at the University of Massachusetts. Practical calibration algorithms are developed in chapter III, and the synthesis technique is refined in chapter IV to reduce side lobes. Chapter V presents the first known images by this class of remote sensing radiometer, and the concluding chapter suggests avenues for future research.

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