TY - GEN
T1 - Fixed-order controller design for state space polytopic systems by convex optimization
AU - Karimi, Alireza
AU - Sadabadi, Mahdieh Sadat
PY - 2013/2/23
Y1 - 2013/2/23
N2 - In this paper, a new method for fixed-order controller design of systems with polytopic uncertainty in their state space representation is proposed. The approach uses the strictly positive realness (SPRness) of some transfer functions, as a tool to decouple the controller parameters and the Lyapunov matrices and represent the stability conditions and the performance criteria by a set of linear matrix inequalities. The quality of this convex approximation depends on the choice of a central state matrix. It is shown that this central matrix can be computed from a set of initial fixed-order controllers computed for each vertex of the polytope. The stability of the closed-loop polytopic system is guaranteed by a linear parameter dependent Lyapunov matrix. The results are extended to fixed-order H∞ controller design for SISO systems.
AB - In this paper, a new method for fixed-order controller design of systems with polytopic uncertainty in their state space representation is proposed. The approach uses the strictly positive realness (SPRness) of some transfer functions, as a tool to decouple the controller parameters and the Lyapunov matrices and represent the stability conditions and the performance criteria by a set of linear matrix inequalities. The quality of this convex approximation depends on the choice of a central state matrix. It is shown that this central matrix can be computed from a set of initial fixed-order controllers computed for each vertex of the polytope. The stability of the closed-loop polytopic system is guaranteed by a linear parameter dependent Lyapunov matrix. The results are extended to fixed-order H∞ controller design for SISO systems.
UR - http://www.scopus.com/inward/record.url?scp=84881069075&partnerID=8YFLogxK
U2 - 10.3182/20130204-3-FR-2033.00194
DO - 10.3182/20130204-3-FR-2033.00194
M3 - Conference contribution
AN - SCOPUS:84881069075
SN - 9783902823250
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
SP - 683
EP - 688
BT - IFAC Joint conference SSSC,FDA, TDS - 5th IFAC Symposium on System Structure and Control, SSSC 2013
A2 - Witrant, Emmanuel
A2 - Martinez-Molina, John-Jairo
A2 - Lovera, Marco
A2 - Sename, Olivier
A2 - Dugard, Luc
PB - International Federation of Automatic Control (IFAC)
T2 - 5th IFAC Symposium on System Structure and Control, SSSC 2013
Y2 - 4 February 2013 through 6 February 2013
ER -