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This volume updates purely mathematical theoretical aspects, and it also presents concrete examples of the wide range of applications of matrix theory in other disciplines. Nonlinear system analysis is of interest to engineers, sociologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. In mathematics, a nonlinear system does not satisfy the superposition principle such as in a linear system. Therefore, the theories underlining nonlinear analysis and their applications need to be developed on their own merit. The first section of this book is a collection of examples reporting recent advances in both theory and applications of nonlinear system analysis. The contents of each chapter will provide in-depth foresight to interested readers. As numerical linearization to a set of matrix equations is still the principal method used to solve a nonlinear system, matrix analysis is the topic of the second section of this book. The matrices have invaded practically all areas of mathematics, the experimental and social sciences, engineering, and technology. Nonlinear System Analysis – An Overview of Historical and Recent Advances A Review of Nonlinear Control Strategies for Shape and Stress in Structural Engineering A Type-2 Fuzzy State Observer Model for Non-Stationary Dynamic System Identification: An Incremental Learning Method with Noise Handling Bringing Data Converter Pairs into Chaotic Oscillation for Built-in Self-Test and Entropy Generation Behavioral Analysis of Nonlinear Systems and the Effect of Noise on These Systems Exploring the Non-Linear Relationship between Economic Growth and Its Main Drivers over the Last Decade in EU: Evidence from a Panel Smooth Transition Regression To Be or Not to Be Connected: Reconstructing Nonlinear Dynamical System Structure Families of Seventh-Order KdV Equations Having Traveling Wave and Soliton Solutions Numerical Solutions of Nonlinear Schrödinger Equation: An Application Example of Nonlinear Analysis On Two-Step Hybrid Numerical-Butterfly Optimization Technique for System of Nonlinear Equations in Banach Space Enhancing Regression Analysis with Splines and Machine Learning – Evaluation of How to Capture Complex Non-Linear Multidimensional Variables The Matrices, Their History, Importance and Applications Eigenvalues of Matrices in Chemical Kinetics and Their Algebraic and Geometric Multiplicities Matrices with a Diagonal Commutator On the Universal Realizability Problem: New Results