Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.

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Convex bodies : the Brunn-Minkowski theory

In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire

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Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods

This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

Algorithms in Combinatorial Geometry

A numerically stable and fairly fast scheme is described to compute the unitary matrices U and V which transform a given matrix A into a diagonal form $\Sigma = U^ * AV$, thus exhibiting A’s singular values on $\Sigma $’s diagonal. The scheme first transforms A to a bidiagonal matrix J, then diagonalizes J. The scheme described here is complicated but does not suffer from the computational difficulties which occasionally afflict some previously known methods. Some applications are mentioned, in particular the use of the pseudo-inverse $A^I = V\Sigma ^I U^* $ to solve least squares problems in a way which dampens spurious oscillation and cancellation.

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Calculating the Singular Values and Pseudo-Inverse of a Matrix

The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars

A Simple Non-Euclidean Geometry and Its Physical Basis

This chapter discusses the dissection graphs of planar point sets. It discusses the general properties of the graphs G k . The graph G k can be constructed as follows. Let l be any oriented line containing no points of S and having k + 1 points of S on its positive side. l is to be translated to its left until it meets a point p 1 of S . This line will be called l (0). Then, l (0) is to be rotated counterclockwise by θ about p 1 into line l (θ) until it meets a second point p 2 of S at l (θ 1 ) = 1 1 . l (0) is then rotated counterclockwise about p 2 until l (θ) meets a point p 3 of S at l (θ 2 ) = l 2 , etc. This gives a sequence of points p 1 , p 2 , …, p n of S with p N +1 = p 1 , p N +2 = p 2 and a sequence of directed lines l 1 , l 2 , l N , l N +1 with l N +2 = l 1 .

Dissection Graphs of Planar Point Sets

Corrections and Additional Remarks to our Paper: The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars

1. The fixed point theorem. Let T: X^> Y be a point-to-set function and let T~l: Y—>X be the point-to-set function such that xET~l(y) if and only if yET(x). If X and Y are topological spaces, T is continuous provided the function T~l is both open and closed, and each set T(x) is closed. Let H be Cech homology theory with coefficients in a field, and let En be Euclidean w-space. A mapping /: 5—>£„ will be said to link a point of En provided that x£/(5) and the induced homomorphism /*: Hn_i(B)—>i7„_i(£„ — x) is not zero.

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Ernst Straus

Papers

The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars

A Simple Non-Euclidean Geometry and Its Physical Basis

Dissection Graphs of Planar Point Sets

Corrections and Additional Remarks to our Paper: The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars

A fixed point theorem