ml_ct_ss_partstab
Stabilizing feedback for standard systems.
Contents
Syntax
[K, info] = ml_ct_ss_partstab(A, B) [K, info] = ml_ct_ss_partstab(A, B, opts)
Description
Partial stabilization is used for the continuous-time system of odinary differential equations
x'(t) = Ax(t) + Bu(t) (1)
to get a stabilizing feedback term K, such that all eigenvalues of A-B*K are in the open left half-plane. It is assumed that A has no eigenvalues on the imaginary axis.
Input
A - matrix with dimensions n x n in (1) B - matrix with dimensions n x m in (1) opts - structure, containing the following optional entries:
Parameter | Meaning |
Beta | nonnegative scalar, used as shift of the in Bass' algorithm for better conditioning if StabMethod == 'lyap' is chosen default: 0.1 |
StabMethod | character array, determining algorithm for the partial stabilization
|
stabmethodopts | structure, containing the optional parameters for the sign function based Lyapunov or Bernoulli equation solver used for the stabilization, see ml_abe_sgn or ml_lyap_sgn default: struct() |
stabsignmopts | structure, containing the optional parameters for the matrix sign function used for the decomposition into stable and anti-stable system parts, see ml_signm default: struct() |
UnstabDim | integer, dimension of the deflating anti-stable subspace, negative if unknown default: -1 |
Output
K - stabilizing feedback matrix of dimensions m x n info - structure, containing the following information about the partial stabilization method
Entry | Meaning |
infoSTABMETH | structure, containing information about the sign function based solver used for the stabilization, see ml_abe_sgn or ml_lyap_sgn |
infoSTABMETH2 | structure, containing information about the sign function based solver used for a second stabilization if necessary, see ml_abe_sgn or ml_lyap_sgn |
infoSTABSIGNM | structure, containing information about the matrix sign function method used for the decomposition, see ml_signm |
infoSTABSIGNM2 | structure, containing information about the matrix sign function method used for the a second decomposition, see ml_signm |
Method | character array, shortcut of the used stabilization algorithm, with 'abe' for the algebraic Bernoulli equation and 'lyap' for Bass' algorithm |
Ns | Number of identified stable eigenvalues |
Nu | Number of identified anti-stable eigenvalues |
Reference
P. Benner, Partial stabilization of descriptor systems using spectral projectors, in: P. Van Dooren, S. P. Bhattacharyya, R. H. Chan, V. Olshevsky, A.Routray (Eds.), Numerical Linear Algebra in Signals, Systems and Control, Vol. 80 of Lect. Notes Electr. Eng., Springer Netherlands, 2011, pp. 55--76. https://doi.org/10.1007/978-94-007-0602-6_3
See Also