ml_ct_dss_partstab
Stabilizing feedback for descriptor systems.
Contents
Syntax
[K, info] = ml_ct_dss_partstab(A, B, E) [K, info] = ml_ct_dss_partstab(A, B, E, opts)
Description
Partial stabilization is used for the continuous-time system of differential-algebraic equations
Ex'(t) = Ax(t) + Bu(t) (1)
to get a stabilizing feedback term K, such that all finite eigenvalues of s*E - A + B*K are in the left open half-plane. It is assumed that the pencil s*E - 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)
- E - matrix with dimensions n x n in (1)
- opts - structure, containing the following optional entries:
Parameter | Meaning |
Beta | nonnegative scalar, used as shift of the Bass' algorithm for better conditioning if StabMethod == 'lyap' is chosen 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() |
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_cabe_sgn or ml_lyap_sgn 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 sign function based solver used for the stabilization, see ml_cabe_sgn or ml_lyap_sgn |
infoSTABMETH2 | structure, containing information about the sign function based solver used for a second stabilization if necessary, see ml_cabe_sgn or ml_lyap_sgn |
Method | character array, shortcut of the used stabilization algorithm, with 'cabe' for the algebraic Bernoulli equation and 'lyap' for Bass' algorithm |
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