Stabilization of large linear systems

• Main Authors: He, C., Mehrmann, V.
• Other Authors: TU Chemnitz, SFB 393
• Format: Others
• Language: English
• Published: Universitätsbibliothek Chemnitz 1998
• Subjects: Riccati equation; stabilization; linear; multi-input; control system; MSC 65F05; ddc:510
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800595; http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800595; http://www.qucosa.de/fileadmin/data/qucosa/documents/4138/data/b021.pdf; http://www.qucosa.de/fileadmin/data/qucosa/documents/4138/data/b021.ps; http://www.qucosa.de/fileadmin/data/qucosa/documents/4138/19980059.txt

We discuss numerical methods for the stabilization of large linear multi-input control systems of the form x=Ax + Bu via a feedback of the form u=Fx. The method discussed in this paper is a stabilization algorithm that is based on subspace splitting. This splitting is done via the matrix sign-function method. Then a projection into the unstable subspace is performed followed by a stabilization technique via the solution of an appropriate algebraic Riccati equation. There are several possibilities to deal with the freedom in the choice of the feedback as well as in the cost functional used in the Riccati equation. We discuss several optimality criteria and show that in special cases the feedback matrix F of minimal spectral norm is obtained via the Riccati equation with the zero constant term. A theoretical analysis about the distance to instability of the closed loop system is given and furthermore numerical examples are presented that support the practical experience with this method.