Subject description - XP35LMI1

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XP35LMI1 Linear matrix inequalities
Roles:S, PV Extent of teaching:2P+2C
Department:13135 Language of teaching:EN
Guarantors:Henrion D. Completion:ZK
Lecturers:Henrion D. Credits:4
Tutors:Henrion D. Semester:


Semidefinite programming or optimization over linear matrix inequalities (LMIs) is an extension of linear programming to the cone of positive semidefinite matrices. LMI methods are an important modern tool in systems control and signal processing. Theory: Convex sets represented via LMIs; LMI relaxations for solution of non-convex polynomial optimization problems; Interior-point algorithms to solve LMI problems; Solvers and software; LMIs for polynomial mehods in control. Control applications: robustness analysis of linear and nonlinear systems; design of fixed-order robust controllers with H-infinity specifications. For more information, see

Výsledek studentské ankety předmětu je zde: XP35LMI

Course outlines:

Exercises outline:


# S. Boyd, L. Vandenberghe. Convex Optimization, Cambridge University Press, 2005 # A. Ben-Tal, A. Nemirovskii. Lectures on modern convex optimization: analysis, algorithms and engineering applications. SIAM, Philadelphia,
2001. Most of the material there can be found in various lecture notes and
slides available at A. Nemirovksii's webpage at Georgia Tech. LMI representation of semialgebraic sets and lift-and-project techniques are described in: # A. Ben-Tal, A. Nemirovskii. Lectures on modern convex optimization: analysis, algorithms and engineering applications. SIAM, Philadelphia, 2001 # P. A. Parrilo, S. Lall. SDP Relaxations and Algebraic Optimization in Control. ECC'03 and CDC'03 workshops, whose slides are available at P. A. Parrilo's webpage at MIT. Modern state-space LMI methods in control are nicely surveyed in: # C. Scherer, S. Weiland. LMIs in Control, Lecture Notes at Delft University of Technology and Eindhoven University of Technology, 2005. Polynomials methods for robustness analysis are well described in # B. R. Barmish. New tools for robustness of linear systems. MacMillan,
1994. Polynomial methods and LMI optimization for fixed-order robust controller
design are described in parts III and IV of: # D. Henrion. Course on polynomial methods for robust control, LAAS-CNRS Toulouse, 2001 as well as in the papers # D. Henrion, M. Sebek, V. Kucera. Positive Polynomials and Robust Stabilization with Fixed-Order Controllers, IEEE Transactions on Automatic Control, Vol. 48, No. 7, pp. 1178-1186, July 2003 # D. Henrion, D. Arzelier, D. Peaucelle. Positive Polynomial Matrices and Improved LMI Robustness Conditions, Automatica, Vol. 39, No. 8, pp. 1479-1485, August 2003.


Subject is included into these academic programs:

Program Branch Role Recommended semester
DOKP Common courses S
DOKK Common courses S
DKYR_2020 Common courses PV

Page updated 16.6.2024 17:52:04, semester: Z,L/2023-4, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)