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Relancer l'économie après la crise induite par la pandémie de COVID 19 nécessite des politiques et des réformes qui s'attaquent aux inégalités et soutiennent l'égalité des chances. Toutefois, la mise en œuvre de telles réformes exige un large soutien de la population. Afin de mieux comprendre les facteurs qui influencent l'adhésion de l'opinion publique, le présent rapport propose une analyse détaillée de la perception qu'ont les individus des inégalités et des préoccupations qu'elles suscitent dans différents pays. Il décrit comment les préoccupations relatives aux inégalités de revenu ont progressé au fil du temps dans les pays de l'OCDE. Aujourd'hui, dans la plupart des pays, une grande majorité de la population considère que les inégalités de revenu sont trop importantes et que la mobilité intergénérationnelle est trop faible. Pourtant, les politiques de réduction des inégalités pourraient ne pas susciter une adhésion suffisante à leur mise en œuvre si la société ne parvient pas à s'accorder sur des solutions politiques concrètes ou si ses membres doutent de l'efficacité de ces mesures. En outre, même lorsque la majorité réclame plus d'égalité, une opinion publique divisée peut compliquer l'introduction de réformes. Le rapport montre que les personnes d'un même pays sont souvent divisées au sujet de l'ampleur des inégalités et de ce qui devrait être fait pour relever ce défi. Il présente comment l'analyse des perceptions et des préoccupations des individus peut être utilisée pour éclairer l'élaboration de l'action des pouvoirs publics.

Matrix inequalities.

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Group Majorization Methods Extensions of Matrix Inequalities to Lie Groups studiesvarious concepts of matrix and inequalities extensions. The book provides the readerwith insights into the Matrix Inequalities and Their Extensions to Lie Groups in orderto give a methodical and efficient account of recent important extensions of classicalmatrix results, especially matrix inequalities.

Matrix inequalities. --- Lie groups.

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Matrices. --- Matrix inequalities. --- Inégalités matricielles. --- Matrices --- Inégalités matricielles --- Matrix inequalities --- Inequalities (Mathematics) --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal

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Control theory. --- Matrix inequalities. --- Mathematical optimization. --- Théorie de la commande --- Inégalités matricielles --- Optimisation mathématique --- Matrix inequalities --- Control theory --- Mathematical optimization --- Inequalities (Mathematics) --- Matrices --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Dynamics --- Machine theory

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This book presents the various design methods of a state-feedback control law and of an observer. The considered systems are of continuous-time and of discrete-time nature, monovariable or multivariable, the last ones being of main consideration. Three different approaches are described: • Linear design methods, with an emphasis on decoupling strategies, and a general formula for multivariable controller or observer design; • Quadratic optimization methods: Linear Quadratic Control (LQC), optimal Kalman filtering, Linear Quadratic Gaussian (LQG) control; • Linear matrix inequalities (LMIs) to solve linear and quadratic problems. The duality between control and observation is taken to advantage and extended up to the mathematical domain. A large number of exercises, all given with their detailed solutions, mostly obtained with MATLAB, reinforce and exemplify the practical orientation of this book. The programs, created by the author for their solving, are available on the Internet sites of Springer and of MathWorks for downloading. This book is targeted at students of Engineering Schools or Universities, at the Master’s level, at engineers desiring to design and implement innovative control methods, and at researchers.

Control theory. --- Electronic books. -- local. --- Mathematical optimization. --- Matrix inequalities. --- Control theory --- Matrix inequalities --- Mathematical optimization --- Mechanical Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Operations Research --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Engineering. --- System theory. --- Applied mathematics. --- Engineering mathematics. --- Control engineering. --- Control. --- Systems Theory, Control. --- Appl.Mathematics/Computational Methods of Engineering. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Inequalities (Mathematics) --- Matrices --- Dynamics --- Machine theory --- Systems theory. --- Control and Systems Theory. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematics --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy