Linear Matrix Inequalities in Control

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course topics Facts from convex analysis. LMI’s: history, algorithms and software. The role of LMI’s in dissipativity, stability and nominal performance. Analysis results. From LMI analysis to LMI synthesis. State-feedback and output-feedback synthesis algorithms From nominal to robust stability, robust performance and robust synthesis. IQC’s and multipliers. Relations to classical tests and to µ-theory. Mixed control problems and parametrically-varying systems and control design. Siep Weiland and Carsten Scherer (DISC) Linear Matrix Inequalities in Control Class 1 6 / 59
homework and grading Exercises Grading One exercise set is issued for every class. All sets have options to choose from Please hand in within 2 weeks. Your average grade over 4 homework sets. Siep Weiland and Carsten Scherer (DISC) Linear Matrix Inequalities in Control Class 1 7 / 59
Page 1 and 2: Linear Matrix Inequalities in Contr
Page 3 and 4: Outline of Part II 2 Convex sets an
Page 5: organization and addresses All mate
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
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Recap: Hermitian and symmetric matr
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Main LMI problems 1 LMI feasibility
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Linear Matrix Inequalities Definiti
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Why are LMI’s interesting? Reason
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Affinely constrained LMI is LMI Com
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First examples in control Example 1
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First examples in control Example 3
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Trusses Trusses consist of straight
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Truss topology design Problem Find
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From truss topology design to LMI
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Yalmip coding for LMI optimization
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Useful software: General purpose MA
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Linear Matrix Inequalities in Control

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