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5.1.1 The Recursive Algorithms
After transforming the given state-space system to the block controller-Hessenberg form  , the recursive algorithm constructs a block upper-triangular matrix  and a block upper-bidiagonal matrix  , whose diagonal blocks  ,  , ...,  contain the eigenvalues to be assigned, such that
 , where  and  has full rank.
The following steps are performed:
1. Set  .
2. Compute the blocks  through  of  recursively as follows:
2.1 Compute  .
2.2 Find the RQ decomposition of  :  .
3. Compute the feedback matrix  by solving the linear system:
 .
Option value for the recursive pole assignment method.
Although the recursive algorithm is the most efficient of all the algorithms, it is not necessarily numerically stable. In the single-input case, however, the algorithm has been proven to be numerically reliable (Arnold and Datta (1998)) in the sense that the ill-conditioning of the matrix  is an indicator of the breakdown of the algorithm. Both the single-input and multi-input algorithms have worked well in most test cases. The RQ version of the single-input algorithm is numerically stable (Arnold and Datta (1998)).
Make sure the application is loaded.
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Load the collection of test examples.
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This is a model of an L-1011 aircraft.
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Here are the desired poles, arbitrarily chosen.
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The multi-input recursive method gives the following feedback gain matrix.
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This computes the norm of the feedback gain matrix.
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Here are the computed closed-loop poles.
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Make sure the function MultipleListPlot is available.
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This displays the closed-loop poles of the L-1011 aircraft model on the complex plane.
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