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

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

Considers stationary stochastic discrete-time vector processes made up of two component processes y and u, such that the joint (y,u)-process has a rational spectral density phi /sub yu/(z). Such processes can be represented by a white noise driven matrix transfer function model, and (in most cases) by a closed-loop model. A number of new results are presented on the connections between these two representations, and on their properties: stability, invertibility, identifiability, uniqueness of the spectral factorization, detection of feedback, and continuity of spectral factors.

New results on stationary stochastic feedback processes

Various optimal control strategies exist in the literature. Prominent approaches are Robust Control and Linear Quadratic Regulators, the first one being related to the H∞ norm of a system, the second one to the H2 norm. In 1994, F. De Bruyne et al [1] showed that assuming knowledge of the poles of a transfer function one can derive upper bounds on the H∞ norm as a constant multiple of its H2 norm. We strengthen these results by providing tight upper bounds also for the case where the transfer functions are restricted to those having a real valued impulse response. Moreover the results are extended by studying spaces consisting of transfer functions with a common denominator polynomial. These spaces, called rational modules, have the feature that their analytic properties, captured in the integral kernel reproducing them, are accessible by means of purely algebraic techniques.

Using H 2 norm to bound H ∞ norm from above on real rational modules

Using the dual Youla parametrizations of controller-based coprime factor plant perturbations and plant-based coprime factor controller perturbations, we characterize the set of all plants that have the same optimal LQG or MV controller.

http://ieeexplore.ieee.org/iel3/4303/12402/00573570.pdf

Parametrization of all plants that have the same optimal LQG controller

https://perso.uclouvain.be/michel.gevers/PublisMig/SYSID12_Diego.pdf

Mean-Squared Error Experiment Design for Linear Regression Models

We prove the uniform asymptotic stability of a new error system, whose transition matrix contains both a regression vector and a filtered version of that vector. We show that stability is under conditions which are different from the usual SPR or small gain requirements. We show that this error system arises from the design of adaptive observers for some classes of time-varying or nonlinear systems.

Michel Gevers

Papers

New results on stationary stochastic feedback processes

Using H 2 norm to bound H ∞ norm from above on real rational modules

Parametrization of all plants that have the same optimal LQG controller

Mean-Squared Error Experiment Design for Linear Regression Models

Exponential convergence of a new error system arising from adaptive observers