ml_dt_dss_partstab
Stabilizing feedback for descriptor systems.
Contents
Syntax
[K, info] = ml_dt_dss_partstab(A, B, E) [K, info] = ml_dt_dss_partstab(A, B, E, opts)
Description
Partial stabilization is used for the discrete-time system of differential-algebraic equations
Ex(t+1) = Ax(t) + Bu(t) (1)
to get a stabilizing feedback term K, such that all finite eigenvalues of s*E - A + B*K are inside the open unit disk. It is assumed that the pencil s*E - 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)
- E - matrix with dimensions n x n 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 |
DecompEig | positive scalar, overestimation of the absolute value of the largest finite eigenvalue of s*E - A, if set, replaces the computation with DecompTol default: [] |
DecompTol | nonnegative scalar, tolerance multiplied with the largest singular value of E to determine the smallest non-quasi-zero singular value of E default: log(n)*eps |
infdecopts | structure, containing the optional parameters for the decomposition of the finite and infinite parts of the system using the disk function and subspace extraction method, see ml_disk and ml_getqz default: struct() |
stabdecopts | structure, containing the optional parameters for the decomposition of the stable and unstable parts of the system using the sign function and subspace extraction method, see ml_signm and ml_getqz default: struct() |
stabmethodopts | structure, containing the optional parameters for the Smith iteration based Lyapunov equation solver used for the stabilization, see ml_dlyap_smith default: struct() |
Output
- K - stabilizing feedback matrix of dimensions m x n
- info - structure, containing the following information about the generalized partial stabilization method
Entry | Meaning |
infoINFDISK | structure, containing information about the disk function method used for the separation of the infinite part, see ml_disk |
infoSTABSIGNM | structure, containing information about the sign function method used for the separation of the unstable part, see ml_signm |
infoSTABSIGNM2 | structure, containing information about the sign function method used for a second separation of the unstable part if necessary, see ml_signm |
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 |
Ninf | Number of identified infinite eigenvalues |
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