This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems.

Contents
Introduction to fractional calculus and fractional-order control

Mathematical prerequisites

Definitions and computation algorithms of fractional-order derivatives and Integrals

Solutions of linear fractional-order differential equations

Approximation of fractional-order operators

Modelling and analysis of multivariable fractional-order transfer function Matrices

State space modelling and analysis of linear fractional-order Systems

Numerical solutions of nonlinear fractional-order differential Equations

Design of fractional-order PID controllers

Frequency domain controller design for multivariable fractional-order Systems

Inverse Laplace transforms involving fractional and irrational Operations

FOTF Toolbox functions and models

Benchmark problems for the assessment of fractional-order differential equation algorithms