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Published in:
1986 | OriginalPaper | Chapter
Minimum energy control. Minimum time-energy feedback controls.
Author : J. P. LaSalle
Published in: The Stability and Control of Discrete Processes
Publisher: Springer New York
Included in: Professional Book Archive
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The positive semidefinite symmetrix matrix 17.1 $$w\left( n \right) = Y\left( n \right){Y^T}\left( n \right) = \sum\limits_{j = 0}^{n - 1} {{A^j}B{B^T}{{\left( {{A^J}} \right)}^T}} $$ introduced in Section 15 plays an important role in the theory of linear control systems and is called the controllability grammian (see Nering [1], p. 150 for the definition of the grammian of a set of vectors; W(n) is the grammian of the matrices B,AB,…,An-1B).