TUM Library

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Authors -- 1 Introduction -- Determinants -- Second-Order Determinant -- Third-Order Determinant -- Minor -- Cofactor -- Properties of Determinants -- Matrices -- Definition -- Order of a Matrix -- Row Matrix -- Column Matrix -- Square Matrix -- Null Matrix -- Principle Diagonal -- Diagonal Matrix -- Unit Matrix or Identity Matrix -- Scalar Matrix -- Upper Triangular Matrix -- Lower Triangular Matrix -- Transpose of a Matrix -- Symmetric Matrix -- Skew Symmetric Matrix

Singular Matrix -- Adjoint of a Matrix -- Inverse of a Matrix -- Equality of Matrix -- Addition of Matrices -- Subtraction of Matrices -- Multiplication of Matrices -- Conjugate of a Matrix -- Hermitian Matrix -- Skew Hermitian Matrix -- Rank of a Matrix -- Definition of Transfer Function -- Limitations of Transfer Function Approach -- Introduction to State Space Analysis -- Input and Output Variables -- State Model -- Review of State Models -- Non-Uniqueness of State Model -- 2 State Space Approach -- Role of Eigen Values and Eigen Vectors -- How to Find Eigen Vectors?

Free and Forced Responses -- Properties of State Transition Matrix -- Evaluation of State Transition Matrix -- Minimal Realization -- Minimal Realization Using Transfer Function Matrix -- Non-Minimal Realization -- Non-Minimal Realization Using Transfer Function Matrix -- Balanced Realization -- 3 State Feedback Control and State Estimator -- Concept of Controllability and Observability -- Controllability -- a) State Controllability -- Condition for Complete State Controllability in the s-Plane -- Output Controllability -- Uncontrollable System -- Stabilizability -- Observability

Complete Observability -- Condition for Complete Observability in the s-Plane -- Detectability -- Kalman's Tests for Controllability and Observability -- State Space Representation in Canonical Forms -- Controllable Canonical Form -- Observable Canonical Form -- Diagonal Canonical Form -- Jordan Canonical Form -- State Feedback Control (Pole Placement Technique) -- Determination of State Feedback Gain Matrix (K(f)) -- State Observers -- Full-Order State Observers -- Reduced-Order State Observers -- Minimum-Order State Observers -- Mathematical Model of an Observer

Determination of State Observer Gain Matrix (K(0)) -- 4 Non-Linear Systems and Phase Plane Analysis -- Characteristics of Non-Linear Systems -- Jump Resonance -- Types of Nonlinearities -- Saturation -- Deadzone -- Backlash -- Friction -- Describing Function Fundamentals -- Describing Function of Deadzone -- Describing Function of Saturation Nonlinearity -- Describing Function of Deadzone and Saturation -- Describing Function of On-Off Controller with a Deadzone -- Describing Function of Backlash Nonlinearity -- Describing Function of Relay with Deadzone and Hysteresis -- Phase Plane Analysis

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 Covers both linear and non-linear system theory Explores state feedback control and state estimator concepts Discusses non-linear systems and phase plane analysis Includes non-linear system stability and bifurcation behaviour Elaborates optimal control and estimation

OCLC-licensed vendor bibliographic record.