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Function Reference: place

Function File: f = place (sys, p)
Function File: f = place (a, b, p)
Function File: [f, info] = place (sys, p, alpha)
Function File: [f, info] = place (a, b, p, alpha)

Pole assignment for a given matrix pair (A,B) such that p = eig (A-B*F). If parameter alpha is specified, poles with real parts (continuous-time) or moduli (discrete-time) below alpha are left untouched.

Inputs

sys
Continuous- or discrete-time LTI system.
a
State matrix (n-by-n) of a continuous-time system.
b
Input matrix (n-by-m) of a continuous-time system.
p
Desired eigenvalues of the closed-loop system state-matrix A-B*F. length (p) <= rows (A).
alpha
Specifies the maximum admissible value, either for real parts or for moduli, of the eigenvalues of A which will not be modified by the eigenvalue assignment algorithm. alpha >= 0 for discrete-time systems.

Outputs

f
State feedback gain matrix.
info
Structure containing additional information.
info.nfp
The number of fixed poles, i.e. eigenvalues of A having real parts less than alpha, or moduli less than alpha. These eigenvalues are not modified by place.
info.nap
The number of assigned eigenvalues. nap = n-nfp-nup.
info.nup
The number of uncontrollable eigenvalues detected by the eigenvalue assignment algorithm.
info.z
The orthogonal matrix z reduces the closed-loop system state matrix A + B*F to upper real Schur form. Note the positive sign in A + B*F.

Note

 
 Place is also suitable to design estimator gains:
 L = place (A.', C.', p).'
 L = place (sys.', p).'   # useful for discrete-time systems

Algorithm
Uses SLICOT SB01BD, Copyright (c) 1996-2025, SLICOT, available under the BSD 3-Clause (License and Disclaimer).

Source Code: place