Pole placement design
K = place(A,B,p)
[K,prec,message] = place(A,B,p)
Given the single- or multi-input system
and a vector
p of desired self-conjugate
closed-loop pole locations,
place computes a gain
K such that the state feedback u =
–Kx places the closed-loop poles at the
p. In other words, the eigenvalues of A – BK match
the entries of
p (up to the ordering).
K = place(A,B,p) places the desired closed-loop poles
p by computing a state-feedback gain matrix
K. All the inputs of the plant are assumed to be control inputs.
The length of
p must match the row size of
for multi-input systems and is based on the algorithm from . This algorithm uses the extra degrees
of freedom to find a solution that minimizes the sensitivity of the
closed-loop poles to perturbations in A or B.
[K,prec,message] = place(A,B,p) returns
an estimate of how closely the eigenvalues of A – BK match
the specified locations
the number of accurate decimal digits in the actual closed-loop poles).
If some nonzero closed-loop pole is more than 10% off from the desired
message contains a warning message.
You can also use
place for estimator gain
selection by transposing the
A matrix and substituting
l = place(A',C',p).'
Pole Placement Design
Consider a state-space system
two inputs, three outputs, and three states. You can compute the feedback
gain matrix needed to place the closed-loop poles at
[-1 -1.23 -5.0] by
p = [-1 -1.23 -5.0]; K = place(a,b,p)
place uses the algorithm of  which, for multi-input systems, optimizes
the choice of eigenvectors for a robust solution.
In high-order problems, some choices of pole locations result in very large gains. The sensitivity problems attached with large gains suggest caution in the use of pole placement techniques. See  for results from numerical testing.
 Kautsky, J., N.K. Nichols, and P. Van Dooren, "Robust Pole Assignment in Linear State Feedback," International Journal of Control, 41 (1985), pp. 1129-1155.
 Laub, A.J. and M. Wette, Algorithms and Software for Pole Assignment and Observers, UCRL-15646 Rev. 1, EE Dept., Univ. of Calif., Santa Barbara, CA, Sept. 1984.