LEAD-LAG ALGORITHMS Table of Contents 1. Introduction 2. Discrete-Time Simulation of First-Order Response 2.2.1 Basic Assumptions 2.2.2 General First-Order Recurrence Formulas 2.2.3 Optimum Recurrence Coefficients for Constant t 2.2.4 Optimum Recurrence Coefficients for Variable t 2.2.5 Discussion 2.3.1 Simplifications Based on Approximations of ez 2.3.2 Finite Differences and Bilinear Substitution 2.3.3 Pre-Warping 2.3.4 Composite Past Value Recurrence 2.3.5 Discussion 3. Discrete-Time Simulation of Second-Order Response 3.2.1 Basic Assumptions 3.2.2 General Second-Order Recurrence Formulas 3.2.3 Optimum Recurrence Coefficients for Second-Order Interpolation 3.2.4 Optimum Recurrence Coefficients for Point-to-Point Interpolation 3.2.5 Discussion 3.3.1 Cascaded First-Order Simulations 3.3.2 Finite Difference Method 3.3.3 Bilinear Substitution 3.3.4 Simplifications Based on Approximations of ez 3.3.5 Discussion APPENDIX A: Recursive Simulation of Feedback Loops APPENDIX B: Discrete-Time Simulation of Nth-Order Response