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

This article introduces the FAO crop model AquaCrop. It simulates attainable yields of major herbaceous crops as a function of water consumption under rainfed, supplemental, deficit, and full irrigation conditions. The growth engine of AquaCrop is water-driven, in that transpiration is calculated first and translated into biomass using a conservative, crop-specific parameter: the biomass water productivity, normalized for atmospheric evaporative demand and air CO 2 concentration. The normalization is to make AquaCrop applicable to diverse locations and seasons. Simulations are performed on thermal time, but can be on calendar time, in daily time-steps. The model uses canopy ground cover instead of leaf area index (LAI) as the basis to calculate transpiration and to separate out soil evaporation from transpiration. Crop yield is calculated as the product of biomass and harvest index (HI). At the start of yield formation period, HI increases linearly with time after a lag phase, until near physiological maturity. Other than for the yield, there is no biomass partitioning into the various organs. Crop responses to water deficits are simulated with four modifiers that are functions of fractional available soil water modulated by evaporative demand, based on the differential sensitivity to water stress of four key plant processes: canopy expansion, stomatal control of transpiration, canopy senescence, and HI. The HI can be modified negatively or positively, depending on stress level, timing, and canopy duration. AquaCrop uses a relatively small number of parameters (explicit and mostly intuitive) and attempts to balance simplicity, accuracy, and robustness. The model is aimed mainly at practitioner-type end-users such as those working for extension services, consulting engineers, governmental agencies, nongovernmental organizations, and various kinds of farmers associations. It is also designed to fit the need of economists and policy specialists who use simple models for planning and scenario analysis.

AquaCrop-The FAO Crop Model to Simulate Yield Response to Water: I. Concepts and Underlying Principles

conditions and an accurate semidefinite programming solver," The Journal of the SDPA family for solving large-scale SDPs," in Handbook on Semidefinite. Semidefinite Programming, Combinatorial. Optimization and Primal semidefinite programming problem Handbook of Semidefinite Programming. Kluwer. Solving Euclidean distance matrix completion problems via semidefinite programming. AY Alfakih, A Khandani, H Wolkowicz. Computational optimization.

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Handbook of Semidefinite Programming

With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating frequencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for high-speed applications is placing higher demands on interconnect performance and highlighted the previously negligible effects of interconnects such as ringing, signal delay, distortion, reflections, and crosstalk. In this review paper various high-speed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of high-speed interconnects using model-reduction-based algorithms is discussed in detail.

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Simulation of high-speed interconnects

The probabilistic finite element method (PFEM) is formulated for linear and non-linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non-linear continua.

The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem and a two-dimensional plane-stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Random field finite elements

Analysis and synthesis

Fire protection engineers and preservation architects have long recognized the difficulty in applying building and fire codes to historic buildings. Small, older buildings of significant historic value need an efficient approach to performance-based evaluation. One technique that has gained acceptance is fire risk indexing. The Historic Fire Risk Index described in this paper uses a linear additive model of multiple attribute evaluation to produce a measure of relative fire risk. Weights are established to indicate the importance or significance of fire risk parameters. Then, for each specific historic structure, parameter grades, i.e., the amount or degree that a parameter is present, are determined from information collected in a detailed site survey. Fire risk is evaluated by the scalar product of the parameter weights and grades, producing a single numerical value representing the level of fire safety provided in the building. This is a more rational and more transparent method than the risk indexing systems currently published in model codes and standards.

Fire Risk Index for Historic Buildings

The risk assessment chapters in this section describe concepts and methods to be used in answering the three questions: What could happen? How bad would it be? How likely is it? This chapter in particular is intended to provide an overview of fire risk analysis as a whole, indicating how the subsequent chapters fit together and how a completed fire risk analysis connects to other evaluative and management activities. The purpose of this introductory chapter is threefold:

Introduction to Fire Risk Analysis

Evaluation of Fire Safety: Rasbash/Evaluation of Fire Safety

The problem of developing an expedient, yet credible approach to fire safety evaluation is addressed. Techniques of multiattribute evaluation from the field of management science offer a promising solution to this difficulty. The use of multiattribute evaluation in fire safety is described including techniques that are unique to this type of problem. Details are given on the identification of attributes, assigning attribute weights and values, and selecting an evaluation model. A five-step process for constructing a multiattribute model of fire safety evaluation is presented. The resulting robust structure can provide a means of coupling \"hard fire safety science with inclusive fire risk assessment.

John M. Watts

Papers

Analysis and synthesis

Fire Risk Index for Historic Buildings

Introduction to Fire Risk Analysis

Evaluation of Fire Safety: Rasbash/Evaluation of Fire Safety

Fire Risk Assessment Using Multiattribute Evaluation