Introduction to Mathematical Systems Theory: Discrete time Linear Systems, Control and Identification

Description

Preface Preface to the Second Edition Contents 1 Dynamical Systems 1.1 Introduction 1.2 Systems and Laws 1.3 State Representations 1.4 Illustration 2 Input-Output Systems 2.1 Inputs and Outputs in the Time Domain 2.2 Frequency Domain and Transfer Functions 2.3 State Space Models 2.4 Equivalent and Minimal Realizations 2.5 The Restricted Shift Realization 3 State Space Models 3.1 Controllability 3.2 Observability 3.3 Structure Theory of Realizations 3.4 An Algorithm for Minimal Realizations 3.5 The Subspace Identification Algorithm 3.6 An Example 4 Stability 4.1 Internal Stability 4.2 Input-Output Stability 4.3 Stabilization by State Feedback 4.4 Stabilization by Output Feedback 5 Optimal Control 5.1 Problem Statement 5.2 Dynamic Programming 5.3 Linear Quadratic Control 6 Stochastic Systems 6.1 Modelling 6.2 Stationary Processes 6.3 ARMA Processes 6.4 State Space Models 6.5 Spectra and the Frequency Domain 6.6 Stochastic Input-Output Systems 7 Filtering and Prediction 7.1 The Filtering Problem 7.2 Spectral Filtering 7.3 The Kalman Filter 7.4 The Steady State Filter 8 Stochastic Control 8.1 Introduction 8.2 Stochastic Dynamic Programming 8.3 LQG Control with State Feedback 8.4 LQG Control with Output Feedback 9 System Identification 9.1 Identification 9.2 Regression Models 9.3 Maximum Likelihood 9.4 Estimation of Autoregressive Models 9.5 Estimation of ARMAX Models 9.6 Model Validation 9.6.1 Lag Orders 9.6.2 Residual Tests 9.6.3 Inputs and Outputs 9.6.4 Model Selection 10 Cycles and Trends 10.1 The Periodogram 10.2 Spectral Identification 10.3 Trends 10.4 Seasonality and Nonlinearities 11 Further Developments 11.1 Continuous Time Systems 11.2 Optimal Control 11.3 Nonlinear Systems 11.3.1 Applications in Life Sciences 11.4 Infinite Dimensional Systems 11.5 Robust and Adaptive Control 11.6 Stochastic Systems 11.7 Networked Systems 11.8 Hybrid Systems 11.9 System Identification Bibliography Index