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

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

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

ml_ct_ss_partstab | ml_ct_dss_partstab