Stephen L.Campbell is Professor of Mathematics at North Carolina State University. Ramine Nikoukhah is Senior Scientist (Directeur de Recherche) at Institut National de Recherche en Informatique et en Automatique (INRIA) in France.

"Aimed at a broad audience that includes graduate students in engineering and applied mathematics, the book is notable for its emphasis and focus on mathematical intuition and numerical issues. It is very well written, with an attention to detail and rigor... [T]he material is accessible to a wide audience with interests in areas such as control theory of differential equations."--Bogdan I. Epureanu, IEEE Control Systems

• Preface vii Chapter 1. Introduction 1 1.1 The Basic Question 1 1.2 Failure etection 3 1.3 Failure Identification 9 1.4 Active Approach versus Passive Approach 10 1.5 Outline of the Book 13 Chapter 2. Failure Detection 14 2.1 Introduction 14 2.2 Static Case 15 2.3 Continuous-Time Systems 25 2.4 iscrete-Time Systems 36 2.5 Real-Time Implementation Issues 42 2.6 Useful Results 44 Chapter 3. Multimodel Formulation 59 3.1 Introduction 59 3.2 Static Case 60 3.3 Continuous-Time Case 76 3.4 Case of On-line Measured Input 90 3.5 More GeneralCost Functions 92 3.6 iscrete-Time Case 99 3.7 Suspension Example 102 3.8 Asymptotic Behavior 111 3.9 Useful Results 112 Chapter 4. Direct Optimization Formulations 122 4.1 Introduction 122 4.2 Optimization Formulation for Two Models 123 4.3 General-ModelCase 138 4.4 Early etection 142 4.5 Other Extensions 150 4.6 Systems with Delays 155 4.7 Setting Error Bounds 172 4.8 Model Uncertainty 173 Chapter 5. Remaining Problems and Extensions 176 5.1 Direct Extensions 177 5.2 Hybrid and Sampled Data Systems 179 5.3 Relation to Stochastic Modeling 179 Chapter 6. Scilab Programs 181 6.1 Introduction 181 6.2 Riccati-based Solution 181 6.3 The Block iagonalization Approach 185 6.4 Getting Scilab and the Programs 188 Appendix A. List of Symbols 189 Bibliography 193 Index 201

Stephen L.Campbell is Professor of Mathematics at North Carolina State University. Ramine Nikoukhah is Senior Scientist (Directeur de Recherche) at Institut National de Recherche en Informatique et en Automatique (INRIA) in France.

"Aimed at a broad audience that includes graduate students in engineering and applied mathematics, the book is notable for its emphasis and focus on mathematical intuition and numerical issues. It is very well written, with an attention to detail and rigor... [T]he material is accessible to a wide audience with interests in areas such as control theory of differential equations."--Bogdan I. Epureanu, IEEE Control Systems

• Preface vii Chapter 1. Introduction 1 1.1 The Basic Question 1 1.2 Failure etection 3 1.3 Failure Identification 9 1.4 Active Approach versus Passive Approach 10 1.5 Outline of the Book 13 Chapter 2. Failure Detection 14 2.1 Introduction 14 2.2 Static Case 15 2.3 Continuous-Time Systems 25 2.4 iscrete-Time Systems 36 2.5 Real-Time Implementation Issues 42 2.6 Useful Results 44 Chapter 3. Multimodel Formulation 59 3.1 Introduction 59 3.2 Static Case 60 3.3 Continuous-Time Case 76 3.4 Case of On-line Measured Input 90 3.5 More GeneralCost Functions 92 3.6 iscrete-Time Case 99 3.7 Suspension Example 102 3.8 Asymptotic Behavior 111 3.9 Useful Results 112 Chapter 4. Direct Optimization Formulations 122 4.1 Introduction 122 4.2 Optimization Formulation for Two Models 123 4.3 General-ModelCase 138 4.4 Early etection 142 4.5 Other Extensions 150 4.6 Systems with Delays 155 4.7 Setting Error Bounds 172 4.8 Model Uncertainty 173 Chapter 5. Remaining Problems and Extensions 176 5.1 Direct Extensions 177 5.2 Hybrid and Sampled Data Systems 179 5.3 Relation to Stochastic Modeling 179 Chapter 6. Scilab Programs 181 6.1 Introduction 181 6.2 Riccati-based Solution 181 6.3 The Block iagonalization Approach 185 6.4 Getting Scilab and the Programs 188 Appendix A. List of Symbols 189 Bibliography 193 Index 201

Stephen L.Campbell is Professor of Mathematics at North Carolina State University. Ramine Nikoukhah is Senior Scientist (Directeur de Recherche) at Institut National de Recherche en Informatique et en Automatique (INRIA) in France.

"Aimed at a broad audience that includes graduate students in engineering and applied mathematics, the book is notable for its emphasis and focus on mathematical intuition and numerical issues. It is very well written, with an attention to detail and rigor... [T]he material is accessible to a wide audience with interests in areas such as control theory of differential equations."--Bogdan I. Epureanu, IEEE Control Systems

• Preface vii Chapter 1. Introduction 1 1.1 The Basic Question 1 1.2 Failure etection 3 1.3 Failure Identification 9 1.4 Active Approach versus Passive Approach 10 1.5 Outline of the Book 13 Chapter 2. Failure Detection 14 2.1 Introduction 14 2.2 Static Case 15 2.3 Continuous-Time Systems 25 2.4 iscrete-Time Systems 36 2.5 Real-Time Implementation Issues 42 2.6 Useful Results 44 Chapter 3. Multimodel Formulation 59 3.1 Introduction 59 3.2 Static Case 60 3.3 Continuous-Time Case 76 3.4 Case of On-line Measured Input 90 3.5 More GeneralCost Functions 92 3.6 iscrete-Time Case 99 3.7 Suspension Example 102 3.8 Asymptotic Behavior 111 3.9 Useful Results 112 Chapter 4. Direct Optimization Formulations 122 4.1 Introduction 122 4.2 Optimization Formulation for Two Models 123 4.3 General-ModelCase 138 4.4 Early etection 142 4.5 Other Extensions 150 4.6 Systems with Delays 155 4.7 Setting Error Bounds 172 4.8 Model Uncertainty 173 Chapter 5. Remaining Problems and Extensions 176 5.1 Direct Extensions 177 5.2 Hybrid and Sampled Data Systems 179 5.3 Relation to Stochastic Modeling 179 Chapter 6. Scilab Programs 181 6.1 Introduction 181 6.2 Riccati-based Solution 181 6.3 The Block iagonalization Approach 185 6.4 Getting Scilab and the Programs 188 Appendix A. List of Symbols 189 Bibliography 193 Index 201