REPRESENTATION AND REALIZATION OF TIME-VARIABLE LINEAR SYSTEMS
COLUMBIA UNIV NEW YORK DEPT OF ELECTRICAL ENGINEERING
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This research emphasizes those system properties and concepts that can be characterized without solving time-variable differential equations. Criteria are developed for determining the degree of controllability and observability of a time-variable system. These criteria are based on the rank of the controllability and observability matrices, newly defined quantities formed from the system coefficient matrices and a finite number of their derivatives. Based on the theory of equivalent systems and the criteria for controllability and observability, a new approach to the synthesis of nonstationary impulse response matrices is developed. This method of synthesis, which does not require an a priori assumption of separability, provides a systematic procedure for realizing a wide class of impulse responses. By relating the concepts of controllability and unilateral transmission, the existence of a class of unilateral networks composed solely of two-terminal RC time-variable components is demonstrated. A stable example of such a network is presented and possible applications discussed.
- Theoretical Mathematics