QCR:

Path: Common/Control

% Creates a linear quadratic regulator from a state space system.
 
   Create a regulator of the form
   u = -Kx minimizing the cost functional
   J = †{(1/2)[u'ru + x'qx] + u'nx + x'nu}dt.

   Given the constraint:
   .
   x = ax + bu

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   Form:
   [k, sinf] = QCR( a, b, q, r, n )
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   ------
   Inputs
   ------
   a                   Plant matrix                              (N,N)
   b                   Input matrix                              (N,M)
   q                   State cost matrix                         (N,N)
   r                   Input cost matrix                         (M,M)
   n                   State/input cost cross-coupling matrix    (N,M)

   -------
   Outputs
   -------
   k                   Optimal gain
   sinf                Solution to the matrix Ricatti equation

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   References: Franklin, G.F., J.D. Powell, M.L. Workman, Digital Control
               of Dynamic Systems, 2nd Edition, Addison-Wesley, 1990,
               pp. 435-438.
--------------------------------------------------------------------------

Children:

Common: Control/Riccati
Math: MathUtils/Odd

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