Linear Matrix Inequalities in Control

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Part I Course organization Siep Weiland and Carsten Scherer (DISC) Linear Matrix Inequalities in Control Class 1 4 / 59
organization and addresses All material and info is posted on website: w3.ele.tue.nl/nl/cs/education/courses/DISClmi/ Lectures: December 15, 2008 January 5, 2009 January 12, 2009 January 19, 2009 How to contact us Siep Weiland Department of Electrical Engineering Eindhoven University of Technology P.O. Box 513; 5600 MB Eindhoven Phone: +31.40.2475979; Email: s.weiland@tue.nl Carsten Scherer Delft Center for Systems and Control Delft University of Technology Mekelweg 2; 2628 CD Delft Phone: +31-15-2785899; Email: c.w.scherer@tudelft.nl Siep Weiland and Carsten Scherer (DISC) Linear Matrix Inequalities in Control Class 1 5 / 59
Page 1 and 2: Linear Matrix Inequalities in Contr
Page 3: Outline of Part II 2 Convex sets an
Page 7 and 8: homework and grading Exercises Grad
Page 9 and 10: Merging control and optimization In
Page 11 and 12: Optimization problems Casting optim
Page 13 and 14: Optimization problems 1 What is lea
Page 15 and 16: Optimization problems 1 What is lea
Page 17 and 18: A classical result Theorem (Weierst
Page 19 and 20: Convex sets Definition A set S in a
Page 21 and 22: Basic properties of convex sets The
Page 23 and 24: The convex hull Definition The conv
Page 25 and 26: Convex functions Definition A funct
Page 27 and 28: Affine sets Definition A subset S o
Page 29 and 30: Affine functions Definition A funct
Page 31 and 32: Why is convexity interesting ??? Re
Page 37 and 38: Ellipsoidal algorithm Aim: Minimize
Page 41 and 42: Why is convexity interesting ??? Ex
Page 43 and 44: Why is convexity interesting ??? Ex
Page 45 and 46: Upper and lower bounds for convex p
Page 47 and 48: Upper and lower bounds for convex p
Page 49 and 50: Example of duality Primal Linear Pr
Page 51 and 52: Karush-Kuhn-Tucker and duality We n
Page 53 and 54: Karush-Kuhn-Tucker and duality Theo
Page 55 and 56:
Karush-Kuhn-Tucker and duality Rema
Page 57 and 58:
Recap: Hermitian and symmetric matr
Page 59 and 60:
Main LMI problems 1 LMI feasibility
Page 61 and 62:
Linear Matrix Inequalities Definiti
Page 63 and 64:
Why are LMI’s interesting? Reason
Page 65 and 66:
Affinely constrained LMI is LMI Com
Page 67 and 68:
First examples in control Example 1
Page 69 and 70:
First examples in control Example 3
Page 71 and 72:
Trusses Trusses consist of straight
Page 73 and 74:
Truss topology design Problem Find
Page 75 and 76:
From truss topology design to LMI
Page 77 and 78:
Yalmip coding for LMI optimization
Page 79 and 80:
Useful software: General purpose MA
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Linear Matrix Inequalities in Control

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