Linear and Non-Linear System Theory

T Thyagarajan, D Kalpana

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000204339
• Edition: 1
• Topic: Mathematics
• Subtopic: Linear & Nonlinear Programming
• Index: Mathematics

Linear and Non-Linear System Theory focuses on the basics of linear and non-linear systems, optimal control and optimal estimation with an objective to understand the basics of state space approach linear and non-linear systems and its analysis thereof. Divided into eight chapters, materials cover an introduction to the advanced topics in the field of linear and non-linear systems, optimal control and estimation supported by mathematical tools, detailed case studies and numerical and exercise problems. This book is aimed at senior undergraduate and graduate students in electrical, instrumentation, electronics, chemical, control engineering and other allied branches of engineering.

Features

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• Covers both linear and non-linear system theory

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• Explores state feedback control and state estimator concepts

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• Discusses non-linear systems and phase plane analysis

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• Includes non-linear system stability and bifurcation behaviour

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• Elaborates optimal control and estimation

1

Introduction

Determinants

Determinants find their usefulness in solving linear systems. The mathematical expressions of linear systems can be simplified by representing them in the form of determinants.

A determinant contains elements that are arranged along horizontal and vertical lines.

Rows: The elements of a determinant that are arranged along horizontal lines form the ‘rows’.

Columns: The elements of a determinant that are arranged along vertical lines form the ‘columns’.

Second-Order Determinant

It consists of four elements, namely, a₁₁,a₁₂,a₂₁ and a₂₂ which are arranged in two rows and two columns and is expressed as follows:

$\left|\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right|=a_{11}{a}_{22}-a_{21}{a}_{12}$

The above determinant cons...