ml_dt_ss_partstab
Stabilizing feedback for standard systems.
Contents
Syntax
[K, info] = ml_dt_ss_partstab(A, B) [K, info] = ml_dt_ss_partstab(A, B, opts)
Description
Partial stabilization is used for the discrete-time system of odinary differential equations
x(t+1) = Ax(t) + Bu(t) (1)
to get a stabilizing feedback term K, such that all eigenvalues of A-B*K are inside the open unit disk. It is assumed that A has no eigenvalues on the unit disk.
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 | positive scalar < 1, used as shift of the Bass' algorithm for better conditioning default: 0.1 |
stabmethodopts | structure, containing the optional parameters for the Smith iteration based Lyapunov equation solver used for the stabilization, see ml_dlyap_smith 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 Smith iteration based solver used for the stabilization, see ml_dlyap_smith |
infoSTABMETH2 | structure, containing information about the Smith iteration based solver used for a second stabilization if necessary, see ml_dlyap_smith |
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 |
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