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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<hr />
<h1 class="refname">slicot_ab08nd</h1>
<hr/>
<h3>Construction of a regular pencil for a given system such that its generalized eigenvalues are invariant zeros of the system.</h3>
<hr/>
<h3>Syntax</h3>
<hr/>
<table summary="syntax" style="width:50%">
<tr>
<td>[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, M, P, A, B, C, D, TOL)</td>
</tr>
</table>
<h3>Input argument</h3>
<hr/>
<dl>
<dt><span class="term">EQUIL</span></dt>
<dd>
<p class="para">'S': Perform balancing (scaling) or 'N': Do not perform balancing.</p>
</dd>
<dt><span class="term">N</span></dt>
<dd>
<p class="para">The number of state variables, i.e., the order of the matrix A.</p>
</dd>
<dt><span class="term">M</span></dt>
<dd>
<p class="para">The number of system inputs.</p>
</dd>
<dt><span class="term">P</span></dt>
<dd>
<p class="para">The number of system outputs.</p>
</dd>
<dt><span class="term">A</span></dt>
<dd>
<p class="para">The leading N-by-N part of this array must contain the state dynamics matrix A of the system.</p>
</dd>
<dt><span class="term">B</span></dt>
<dd>
<p class="para">The leading N-by-M part of this array must contain the input/state matrix B of the system.</p>
</dd>
<dt><span class="term">C</span></dt>
<dd>
<p class="para">The leading P-by-N part of this array must contain the state/output matrix C of the system.</p>
</dd>
<dt><span class="term">D</span></dt>
<dd>
<p class="para">The leading P-by-M part of this array must contain the direct transmission matrix D of the system.</p>
</dd>
<dt><span class="term">TOL</span></dt>
<dd>
<p class="para">A tolerance used in rank decisions.</p>
</dd>
</dl>
<h3>Output argument</h3>
<hr/>
<dl>
<dt><span class="term">NU</span></dt>
<dd>
<p class="para">The number of (finite) invariant zeros.</p>
</dd>
<dt><span class="term">RANK</span></dt>
<dd>
<p class="para">The normal rank of the transfer function matrix.</p>
</dd>
<dt><span class="term">DINFZ</span></dt>
<dd>
<p class="para">The maximum degree of infinite elementary divisors.</p>
</dd>
<dt><span class="term">NKROR</span></dt>
<dd>
<p class="para">The number of right Kronecker indices.</p>
</dd>
<dt><span class="term">NKROL</span></dt>
<dd>
<p class="para">The number of left Kronecker indices.</p>
</dd>
<dt><span class="term">INFZ</span></dt>
<dd>
<p class="para">The leading DINFZ elements of INFZ contain information on the infinite elementary divisors as follows: the system has INFZ(i) infinite elementary divisors of degree i, where i = 1,2,...,DINFZ.</p>
</dd>
<dt><span class="term">KRONR</span></dt>
<dd>
<p class="para">The leading NKROR elements of this array contain the right Kronecker (column) indices.</p>
</dd>
<dt><span class="term">KRONL</span></dt>
<dd>
<p class="para">The leading NKROL elements of this array contain the left Kronecker (row) indices.</p>
</dd>
<dt><span class="term">AF</span></dt>
<dd>
<p class="para">The leading NU-by-NU part of this array contains the coefficient matrix A of the reduced pencil.</p>
</dd>
<dt><span class="term">BF</span></dt>
<dd>
<p class="para">The leading NU-by-NU part of this array contains the coefficient matrix B of the reduced pencil.</p>
</dd>
<dt><span class="term">INFO</span></dt>
<dd>
<p class="para">0: successful exit; if INFO = -i, the i-th argument had an illegal value.</p>
</dd>
</dl>
<h3>Description</h3>
<hr/>
<p></p>
<p>To construct for a linear multivariable system described by a state-space model (A,B,C,D) a regular pencil (A - lambda*B ) which has the invariant zeros of the system as generalized eigenvalues.</p>
<p>The routine also computes the orders of the infinite zeros and the right and left Kronecker indices of the system (A,B,C,D).</p>
<h3>Used function(s)</h3>
<hr/>
AB08ND
<h3>Bibliography</h3>
<hr/>
http://slicot.org/objects/software/shared/doc/AB08ND.html
<h3>Example</h3>
<hr/>
<pre>
<code class = "nelson">N = 6;
M = 2;
P = 3;
TOL = 0.0;
EQUIL = 'N';
%=============================================================================
A = [1.0 0.0 0.0 0.0 0.0 0.0;
0.0 1.0 0.0 0.0 0.0 0.0;
0.0 0.0 3.0 0.0 0.0 0.0;
0.0 0.0 0.0 -4.0 0.0 0.0;
0.0 0.0 0.0 0.0 -1.0 0.0;
0.0 0.0 0.0 0.0 0.0 3.0];
%=============================================================================
B = [0.0 -1.0;
-1.0 0.0;
1.0 -1.0;
0.0 0.0;
0.0 1.0;
-1.0 -1.0];
%=============================================================================
C = [1.0 0.0 0.0 1.0 0.0 0.0;
0.0 1.0 0.0 1.0 0.0 1.0;
0.0 0.0 1.0 0.0 0.0 1.0];
D = [0.0 0.0;
0.0 0.0;
0.0 0.0];
%=============================================================================
% Check the observability and compute the ordered set of the observability indices (call the routine with M = 0).
[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, 0, P, A, B, C, D, TOL)
% Check the controllability and compute the ordered set of the controllability indices (call the routine with P = 0)
[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, M, 0, A, B, C, D, TOL)
% Compute the structural invariants of the given system.
[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, M, P, A, B, C, D, TOL)
</code>
</pre>
<h3>History</h3>
<hr/>
<table summary = "history" style="width:50%">
<tr>
<th>Version</th>
<th>Description</th>
</tr>
<tr>
<td>1.0.0</td>
<td>initial version</td>
</tr>
</table>
<h3>Author</h3>
<hr/>
<p>SLICOT Documentation</p>
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