There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

Conventions and Notation xv Preface xxi Chapter 1. Introduction 1 Chapter 2. Dynamical Systems and Differential Equations 9 Chapter 3. Stability Theory for Nonlinear Dynamical Systems 135 Chapter 4. Advanced Stability Theory 207 Chapter 5. Dissipativity Theory for Nonlinear Dynamical Systems 325 Chapter 6. Stability and Optimality of Feedback Dynamical Systems 411 Chapter 7. Input-Output Stability and Dissipativity 471 Chapter 8. Optimal Nonlinear Feedback Control 511 Chapter 9. Inverse Optimal Control and Integrator Backstepping 557 Chapter 10. Disturbance Rejection Control for Nonlinear Dynamical Systems 603 Chapter 11. Robust Control for Nonlinear Uncertain Systems 649 Chapter 12. Structured Parametric Uncertainty and Parameter-Dependent Lyapunov Functions 719 Chapter 13. Stability and Dissipativity Theory for Discrete-Time Nonlinear Dynamical Systems 763 Chapter 14. Discrete-Time Optimal Nonlinear Feedback Control 845 Bibliography 901 Index 939

Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach

An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered. The H/sup infinity / performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L/sub 2/ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H/sup infinity /-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H/sup infinity /-constrained problem. Both full- and reduced-order design problems are considered with an H/sup infinity / attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given. >

LQG control with an H/sup infinity / performance bound: a Riccati equation approach

Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control

Nonnegative and Compartmental Dynamical Systems

An LQG control-design problem involving a constraint on H∞ disturbance attenuation is considered. The H∞ performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L2 performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H∞-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H∞-constrained problem. Both full- and reduced-order design problems are considered with an H∞ attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given. A more complete version of this paper is given in [41].

Wassim M. Haddad

Papers

Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach

LQG control with an H/sup infinity / performance bound: a Riccati equation approach

Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control

Nonnegative and Compartmental Dynamical Systems

LQG control with an H ∞ performance bound: a riccati equation approach