Introduction to mathematical systems theory

✍ Scribed by Heij C., Ran A., van Schagen F.

• Publisher: Birkhauser
• Year: 2007
• Tongue: English
• Leaves: 176
• Category: Library

✦ Synopsis

This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering; the focus is on discrete time systems. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation. Exercises using MATLAB, presented on an accompanying CD, enhance the main concepts and techniques in the text.

✦ Table of Contents

Contents......Page 5
Preface......Page 9
1.1 Introduction......Page 11
1.2 Systems and Laws......Page 14
1.3 State Representations......Page 16
1.4 Illustration......Page 18
2.1 Inputs and Outputs in the Time Domain......Page 21
2.2 Frequency Domain and Transfer Functions......Page 24
2.3 State Space Models......Page 26
2.4 Equivalent and Minimal Realizations......Page 30
3.1 Controllability......Page 35
3.2 Observability......Page 37
3.3 Structure Theory of Realizations......Page 41
3.4 An Algorithm for Minimal Realizations......Page 44
4.1 Internal Stability......Page 49
4.2 Input-Output Stability......Page 53
4.3 Stabilization by State Feedback......Page 55
4.4 Stabilization by Output Feedback......Page 59
5.1 Problem Statement......Page 63
5.2 Dynamic Programming......Page 66
5.3 Linear Quadratic Control......Page 69
6.1 Modelling......Page 77
6.2 Stationary Processes......Page 78
6.3 ARMA Processes......Page 81
6.4 State Space Models......Page 85
6.5 Spectra and the Frequency Domain......Page 89
6.6 Stochastic Input-Output Systems......Page 91
7.1 The Filtering Problem......Page 93
7.2 Spectral Filtering......Page 96
7.3 The Kalman Filter......Page 99
7.4 The Steady State Filter......Page 106
8.1 Introduction......Page 111
8.2 Stochastic Dynamic Programming......Page 112
8.3 LQG Control with State Feedback......Page 115
8.4 LQG Control with Output Feedback......Page 118
9.1 Identi.cation......Page 125
9.2 Regression Models......Page 126
9.3 Maximum Likelihood......Page 129
9.4 Estimation of Autoregressive Models......Page 131
9.5 Estimation of ARMAX Models......Page 134
9.6 Model Validation......Page 137
10.1 The Periodogram......Page 143
10.2 Spectral Identi.cation......Page 148
10.3 Trends......Page 153
10.4 Seasonality and Nonlinearities......Page 156
11.1 Continuous Time Systems......Page 161
11.2 Optimal Control......Page 162
11.3 Nonlinear Systems......Page 163
11.4 In.nite Dimensional Systems......Page 165
11.5 Robust and Adaptive Control......Page 166
11.6 Stochastic Systems......Page 168
11.7 System Identi.cation......Page 169
Bibliography......Page 171
Index......Page 175