Minimum energy control. Minimum time-energy feedback controls.

Abstract

The positive semidefinite symmetrix matrix

$$w\left( n \right) = Y\left( n \right){Y^T}\left( n \right) = \sum\limits_{j = 0}^{n - 1} {{A^j}B{B^T}{{\left( {{A^J}} \right)}^T}} $$

(17.1)

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,…,A^n-1B).