Minimum energy control. Minimum time-energy feedback controls.

  • J. P. LaSalle
Part of the Applied Mathematical Sciences book series (AMS, volume 62)


The positive semidefinite symmetrix matrix
$$w\left( n \right) = Y\left( n \right){Y^T}\left( n \right) = \sum\limits_{j = 0}^{n - 1} {{A^j}B{B^T}{{\left( {{A^J}} \right)}^T}} $$
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).


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© Springer Science+Business Media New York 1986

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  • J. P. LaSalle

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