An Algebraic Approach to Time Scale Analysis and Control.
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
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An algebraic approach is developed for multiple time scale decomposition of a linear system using the Smith structure of the system matrix viewed as the matrix of functions of a small parameter c. This derivation makes clear that both the necessary and sufficient multiple semi-stability MSST condition, which ensures well-defined multiple time scale behavior and the time-scale-decomposed system structure which approximates the original system are closely related to the so-called Schur complements of a certain matrix. Furthermore, this decomposition has been extended to a larger class of systems, satisfying the so-called multiple semi-simple nullstructure MSSNS condition. The algebraic approach is also applied to examine the questions of the feedback control of the linear systems. Specifically this document presents results on time scale modifications by state feedback. Keywords Theses eigenvalues perturbations.
- Theoretical Mathematics