内容简介：
Time delay systems exist in many engineering fields such as transportation, communication, process engineering and more recently networked control systems. In recent years, time delay systems have attracted recurring interests from research community. Much of the research work has been focused on stability analysis and stabilization of time delay systems using the so-called Lyapunov-Krasovskii functionals and linear matrix inequality (LMI) approach. While the LMI approach does provide an efficient tool for handling systems with delays in state and/or inputs, the LMI based results are mostly only sufficient and only numerical solutions are available. For systems with known single input delay, there have been rather elegant analytical solutions to various problems such as optimal tracking, linear quadratic regulation and H∞ control. We note that discrete-time systems with delays can usually be converted into delay free systems via system augmentation, however, the augmentation approach leads to much higher computational costs, especially for systems of higher state dimension and large delays. For continuous-time systems, time delay problems can in principle be treated by the infinite-dimensional system theory which, however, leads to solutions in terms of Riccati type partial differential equations or operator Riccati equations which are difficult to understand and compute. Some attempts have been made in recent years to derive explicit and efficient solutions for systems with input/output (i/o) delays. These include the study on the H∞ control of systems with multiple input delays based on the stable eigenspace of a Hamlitonian matrix.
图书目录：
1 Krein Space
1.1 Definition of Krein Spaces
1.2 Projections in Krein Spaces
1.3 Kalman Filtering Formulation in Krein Spaces
1.4 Two Basic Problems of Quadratic Forms in Krein Spaces
1.4.1 Problem 1
1.4.2 Problem 2
1.5 Conclusion
2 Optimal Estimation for Systems with Measurement Delays
2.1 Introduction
2.2 Single Measurement Delay Case
2.2.1 Re-organized Measurements
2.2.2 Re-organized Innovation Sequence
2.2.3 Riccati Diｆｆerence Equation
2.2.4 Optimal Estimate (t | t)
2.2.5 Computational Cost
2.3 Multiple Measurement Delays Case
2.3.1 Re-organized Measurements
2.3.2 Re-organized Innovation Sequence
2.3.3 Riccati Equation
2.3.4 Optimal Estimate (t | t)
2.3.5 Numerical Example
2.4 Conclusion
3 Optimal Control for Systems with Input/Output Delays
3.1 Introduction
3.2 Linear Quadratic Regulation
3.2.1 Duality Between Linear Quadratic Regulation and Smoothing Estimation
3.2.2 Solution to Linear Quadratic Regulation
3.3 Output Feedback Control
3.4 Examples
3.5 Conclusion
4 H∞ Estimation for Discrete-Time Systems with Measurement Delays
4.1 Introduction
4.2 H∞ Fixed-Lag Smoothing
4.2.1 An Equivalent H2 Estimation Problem in Krein Space
4.2.2 Re-organized Innovation Sequence
4.2.3 Calculation of the Innovation Covariance
4.2.4 H∞ Fixed-Lag Smoother
4.2.5 Computational Cost Comparison and Example
4.2.6 Simulation Example
4.3 H∞ d-Step Prediction
4.3.1 An Equivalent H2 Problem in Krein Space
4.3.2 Re-organized Innovation
4.3.3 Calculation of the Innovation Covariance
4.3.4 H∞ d-Step Predictor
4.4 H∞ Filtering for Systems with Measurement Delay
4.4.1 Problem Statement
4.4.2 An Equivalent Problem in Krein Space
4.4.3 Re-organized Innovation Sequence
4.4.4 Calculation of the Innovation Covariance Qw(t)
4.4.5 H∞ Filtering
4.5 Conclusion
5 H∞ Control for Discrete-Time Systems with Multiple Input Delays
5.1 Introduction
5.2 H∞ Full-Information Control Problem
5.2.1 Preliminaries
5.2.2 Calculation of v*
5.2.3 Maximizing Solution of JN with Respect to Exogenous Inputs
5.2.4 Main Results
5.3 H∞ Control for Systems with Preview and Single Input Delay
5.3.1 H∞ Control with Single Input Delay
5.3.2 H∞ Control with Preview
5.4 An Example
5.5 Conclusion
6 Linear Estimation for Continuous-Time Systems with Measurement Delays
6.1 Introduction
6.2 Linear Minimum Mean Square Error Estimation for Measurement Delayed Systems
6.2.1 Problem Statement
6.2.2 Re-organized Measurement Sequence
6.2.3 Re-organized Innovation Sequence
6.2.4 Riccati Equation
6.2.5 Optimal Estimate (t | t)
6.2.6 Numerical Example
6.3 H∞ Filtering for Systems with Multiple Delayed Measurements
6.3.1 Problem Statement
6.3.2 An Equivalent Problem in Krein Space
6.3.3 Re-organized Innovation Sequence
6.3.4 Riccati Equation
6.3.5 Main Results
6.3.6 Numerical Example
6.4 H∞ Fixed-Lag Smoothing for Continuous-Time Systems
6.4.1 Problem Statement
6.4.2 An Equivalent H2 Problem in Krein Space
6.4.3 Re-organized Innovation Sequence
6.4.4 Main Results
6.4.5 Examples
6.5 Conclusion
7 H∞ Estimation for Systems with Multiple State and Measurement Delays
7.1 Introduction
7.2 Problem Statements
7.3 H∞ Smoothing
7.3.1 Stochastic System in Krein Space
7.3.2 Sufficient and Necessary Condition for the Existence of an H∞ Smoother
7.3.3 The Calculation of an H∞ Estimator (t, d)
7.4 H∞ Prediction
7.5 Conclusion
8 Optimal and H∞ Control of Continuous-Time Systems with Input/Output Delays
8.1 Introduction
8.2 Linear Quadratic Regulation
8.2.1 Problem Statements
8.2.2 Preliminaries
8.2.3 Solution to the LQR Problem
8.2.4 An Example
8.3 Measurement Feedback Control
8.3.1 Problem Statement
8.3.2 Solution
8.4 H∞ Full-Information Control
8.4.1 Problem Statement
8.4.2 Preliminaries
8.4.3 Calculation of v∗
8.4.4 H∞ Control
8.4.5 Special Cases
8.5 Conclusion
References
Index
