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 matrix K such that the state feedback u = –Kx places the closed-loop poles at the locations 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 A. place works 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 prec, an estimate of how closely the eigenvalues of A – BK match the specified locations p (prec measures 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 location, message contains a warning message.
You can also use place for estimator gain selection by transposing the A matrix and substituting C' for B.
l = place(A',C',p).'
Pole Placement Design
Consider a state-space system (a,b,c,d) with two inputs, three outputs, and three states. You can compute the feedback gain matrix needed to place the closed-loop poles at p = [-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.