Mathematical Systems Theory

Description

Cover (grey) Title page Preface 1 Introduction 1.1 What is mathematical systems theory? 1.2 A brief history 1.3 Brief description of contents 2 Modelling Principles 2.1 Conservation laws 2.2 Phenomenological principles 2.3 Physical principles and laws 2.3.1 Thermodynamics 2.3.2 Mechanics 2.3.3 Electromagnetism 2.4 Examples 2.4.1 Inverted pendulum 2.4.2 Satellite dynamics 2.4.3 Heated bar 2.4.4 Electrical circuit 2.4.5 Population dynamics 2.4.6 Age dependent population dynamics 2.4.7 Bioreactor 2.4.8 Transport of pollution 2.4.9 National economy 3 Linear differential systems 3.1 Linearization 3.2 Solution of linear differential equations 3.3 Impulse and step response 4 System properties 4.1 Stability 4.1.1 Stability in terms of eigenvalues 4.1.2 Routh's criterion 4.1.3 Lyapunov stability 4.1.4 Interval stability 4.1.5 Input-output stability 4.2 Controllability 4.3 Observability 4.4 Realization theory and Hankel matrices 5 State and Output Feedback 5.1 Feedback and stabilizability 5.2 Observers and the separation principle 5.3 Disturbance rejection 6 Input/output representations 6.1 Laplace transforms and their use for linear time-invariant systems 6.1.1 Connection of systems 6.1.2 Rational functions 6.2 Transfer functions and matrices 6.3 Transfer functions and minimal realizations 6.4 Frequency methods 6.4.1 Oscillations 6.4.2 Nyquist and Bode diagrams 7 Linear Difference Systems 8 Extensions and some related topics 8.1 Abstract system descriptions 8.1.1 Behavioral Modelling 8.2 Polynomial representations 8.3 Examples of other kinds of systems 8.3.1 Nonlinear systems 8.3.2 Descriptor systems 8.3.3 Stochastic systems 8.3.4 Automata 8.3.5 Distributed parameter systems 8.3.6 Discrete event systems 8.4 Optimal Control Theory 8.5 Parameter Estimation 8.6 Filter Theory 8.7 Model reduction 8.8 Adaptive and robust control 9 MATLAB exercises 9.1 Problems 9.2 Solutions Dutch translations Bibliography Index