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.

/pdf/linear-matrix-inequalities-in-system-and-control-theory-2q5cf0pqm2.pdf

Linear Matrix Inequalities in System and Control Theory

http://control.disp.uniroma2.it/galeani/CO/materiale/automatica2000.pdf

Survey Constrained model predictive control: Stability and optimality

A new approach is presented to the problem of detecting the number of signals in a multichannel time-series, based on the application of the information theoretic criteria for model selection introduced by Akaike (AIC) and by Schwartz and Rissanen (MDL). Unlike the conventional hypothesis testing based approach, the new approach does not requite any subjective threshold settings; the number of signals is obtained merely by minimizing the AIC or the MDL criteria. Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.

Detection of signals by information theoretic criteria

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

http://www.eeci-institute.eu/GSC2011/Photos-EECI/EECI-GSC-2011-M5/book_AMS.pdf

Optimization Algorithms on Matrix Manifolds

https://www.itk.ntnu.no/fag/fordypning/TK16-filer/Samling1_MorariLee.pdf

Model predictive control: past, present and future

A Branch-and-bound Approach to the Identification Problem*

The author considers the estimation of time-invariant transfer functions in a deterministic set-up and under the typical situation where the true system has a transfer function that is more complex than the parametrized model transfer function. It is shown that, depending on whether the numerator or the denominator of the transfer function model is chosen to be monic, the corresponding least squares estimate will be overbiased or underbiased, in a frequency weighted sense. >

Estimation of transfer functions: underbiased or overbiased?

Direct Closed-Loop Identification of Multi-Input Systems: Variance Analysis

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2005/Fullpapers/02720.pdf

Identification of a two-input system: variance analysis

We consider optimal experiment design for parametric prediction error system identification of linear time-invariant multi-input multi-output systems in closed-loop when the true system is in the model set. The optimization is performed jointly over the controller and the spectrum of the external input. Previously we tackled this problem by parametrizing the set of admissible controller - external input pairs by a finite set of matrix-valued trigonometric moments and derived a description of the set of admissible finite-dimensional moment vectors by a linear matrix inequality. Here we present a way to recover the controller and the power spectrum of the external input from the optimal moment vector. To this end we prove that the central extension of the finite moment sequence yields a feasible solution. This yields the joint power spectrum of the input and the noise vector as an explicit rational function and allows to construct the optimal “controller - external input pair” directly from the optimal moment vector.

/pdf/central-extensions-in-closed-loop-optimal-experiment-design-53s4cb3u5h.pdf

Michel Gevers

Papers

A Branch-and-bound Approach to the Identification Problem*

Estimation of transfer functions: underbiased or overbiased?

Direct Closed-Loop Identification of Multi-Input Systems: Variance Analysis

Identification of a two-input system: variance analysis

Central extensions in closed-loop optimal experiment design