Coursecode: wb2416

Coursename: Linear Matrix Inequalities in Control

ECTS creditpoints: 6

 Faculty of  Mechanical Engineering and Marine Technology

 Lecturer(s): Scherer, prof.dr. C.W.

 Tel.:  015-27 85899

 Catalog data:

·       Semi-definite programming (linear matrix inequalities)

·       Time-varying and non-linear uncertainties

·       Robust stability and nominal/robust performance analysis

·       Integral quadratic constraints

·       LMI controller synthesis

·       Linear parametrically-varying systems

Course year: MSc 1st year

Period: 2B

Hours p/w: 4

Other hours:

Assessment: Paper and computer exercises

Assessm.period(s):

(see academic calendar)

 Prerequisites: wb2420, wb2421, wb2415

 Follow up:

 Detailed description of topics:

·       Brief introduction to optimization theory (convexity, interior point methods)

·       Robust stability tests for time-varying parametric and non-linear uncertainties

·       Integral quadratic constraints as a general paradigm for robustness analysis

·       Nominal performance analysis for various criteria

·       Extensions to robust performance analysis

·       From analysis in terms of linear matrix inequalities to controller synthesis: a general procedure

·       Design of robust controllers: state-feedback and output-feedback control

·       Design of multi-objective controllers

·       Linear-parametrically-varying systems and the design of linear parametrically-varying controllers

 Course material: Lecture notes

References from literature:

S.P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishan, Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics 15, SIAM, Philadelphia, 1994.

 Remarks (specific information about assessment, entry requirements, etc.):

Goals:

The student must be able to:

1. distinguish linear matrix inequality (LMI) problems from convex and nonlinear programs

2. construct LMI regions for nominal stability analysis

3. explain quadratic stability and its inherent conservatism

4. apply robust stability tests with parameter-dependent Lyapunov functions

5. describe robust LMI problems and their appearance in robust control

6. master the translation of robust to nominal LMI problems with Lagrange duality

7. sketch dissipation theory for dynamical system and its implication for performance specifications

8. reproduce nominal and robust LMI characterizations of H-infinity, H2, quadratic-performance, and energy-to-peak performance

9. describe multiplier relaxation for robust LMI problems

10. sketch derivation of generic convexifying transformation for state- and output-feedback controller synthesis

11. master derivation of synthesis inequalities for single- and multi-objective controller design

12. discuss design of gain-scheduling controllers by linear-parameter-varying controller synthesis

 Computer use:

Computer exercises with Matlab "LMI Control Toolbox".

 Laboratory project(s):

 Design content:

 Percentage of design: