Analysis and design of multivariable systems via the Krylov transformation



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The analysis and design of automatic control systems may be divided into the classical and the modern approach. The modern or state variable approach has been the result of early work by Kalman, Bucy, and others. This modern approach has received much attention in recent literature and in academic circles. However, the classical methods of Bode, Black, and others are more often used to approach practical problems. This dissertation bridges this gap via the use of the Krylov transformation. A new insight into Laplace transform inversion is developed. The method of the Heaviside expansion is extended to the modern case. The relationship between Liapunov functions in various reference frames is given. Finally, the power and flexibility of the Krylov transformation is used to design a system in the modern sense to classical design criteria. Several example problems are worked to illustrate the principles involved.