{"product_id":"analysis-and-synthesis-of-faulttolerant-control-systems-9781118541333","title":"Analysis and Synthesis of FaultTolerant Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn recent years, control systems have become more sophisticated in order to meet increased performance and safety requirements for modern technological systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xv  \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003e1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.1 Overview 1\u003c\/p\u003e \u003cp\u003e1.2 Basic Concepts of Faults 2\u003c\/p\u003e \u003cp\u003e1.3 Classification of Fault Detection Methods 3\u003c\/p\u003e \u003cp\u003e1.3.1 Hardware redundancy based fault detection 3\u003c\/p\u003e \u003cp\u003e1.3.2 Plausibility test 3\u003c\/p\u003e \u003cp\u003e1.3.3 Signal-based fault diagnosis 4\u003c\/p\u003e \u003cp\u003e1.3.4 Model-based fault detection 5\u003c\/p\u003e \u003cp\u003e1.4 Types of Fault-Tolerant Control System 8\u003c\/p\u003e \u003cp\u003e1.5 Objectives and Structure of AFTCS 8\u003c\/p\u003e \u003cp\u003e1.6 Classification of Reconfigurable Control Methods 10\u003c\/p\u003e \u003cp\u003e1.6.1 Classification based on control algorithms 10\u003c\/p\u003e \u003cp\u003e1.6.2 Classification based on field of application 11\u003c\/p\u003e \u003cp\u003e1.7 Outline of the Book 11\u003c\/p\u003e \u003cp\u003e1.7.1 Methodology 11\u003c\/p\u003e \u003cp\u003e1.7.2 Chapter organization 12\u003c\/p\u003e \u003cp\u003e1.8 Notes 13\u003c\/p\u003e \u003cp\u003eReferences 13\u003c\/p\u003e \u003cp\u003e2 Fault Diagnosis and Detection 17\u003c\/p\u003e \u003cp\u003e2.1 Introduction 17\u003c\/p\u003e \u003cp\u003e2.2 Related Work 17\u003c\/p\u003e \u003cp\u003e2.2.1 Model-based schemes 17\u003c\/p\u003e \u003cp\u003e2.2.2 Model-free schemes 18\u003c\/p\u003e \u003cp\u003e2.2.3 Probabilistic schemes 19\u003c\/p\u003e \u003cp\u003e2.3 Integrated Approach 19\u003c\/p\u003e \u003cp\u003e2.3.1 Improved multi-sensor data fusion 19\u003c\/p\u003e \u003cp\u003e2.3.2 Unscented transformation 21\u003c\/p\u003e \u003cp\u003e2.3.3 Unscented Kalman filter 22\u003c\/p\u003e \u003cp\u003e2.3.4 Parameter estimation 23\u003c\/p\u003e \u003cp\u003e2.3.5 Multi-sensor integration architectures 24\u003c\/p\u003e \u003cp\u003e2.4 Robust Unscented Kalman Filter 26\u003c\/p\u003e \u003cp\u003e2.4.1 Introduction 26\u003c\/p\u003e \u003cp\u003e2.4.2 Problem formulation 28\u003c\/p\u003e \u003cp\u003e2.4.3 Residual generation 29\u003c\/p\u003e \u003cp\u003e2.4.4 Residual evaluation 29\u003c\/p\u003e \u003cp\u003e2.5 Quadruple Tank System 30\u003c\/p\u003e \u003cp\u003e2.5.1 Model of the QTS 31\u003c\/p\u003e \u003cp\u003e2.5.2 Fault scenarios in QTS 32\u003c\/p\u003e \u003cp\u003e2.5.3 Implementation structure of UKF 33\u003c\/p\u003e \u003cp\u003e2.5.4 UKF with centralized multi-sensor data fusion 35\u003c\/p\u003e \u003cp\u003e2.5.5 UKF with decentralized multi-sensor data fusion 35\u003c\/p\u003e \u003cp\u003e2.5.6 Drift detection 35\u003c\/p\u003e \u003cp\u003e2.6 Industrial Utility Boiler 38\u003c\/p\u003e \u003cp\u003e2.6.1 Steam flow dynamics 38\u003c\/p\u003e \u003cp\u003e2.6.2 Drum pressure dynamics 40\u003c\/p\u003e \u003cp\u003e2.6.3 Drum level dynamics 40\u003c\/p\u003e \u003cp\u003e2.6.4 Steam temperature 41\u003c\/p\u003e \u003cp\u003e2.6.5 Fault model for the utility boiler 42\u003c\/p\u003e \u003cp\u003e2.6.6 Fault scenarios in the utility boiler 43\u003c\/p\u003e \u003cp\u003e2.6.7 UKF with centralized multi-sensor data fusion 43\u003c\/p\u003e \u003cp\u003e2.6.8 UKF with decentralized multi-sensor data fusion 43\u003c\/p\u003e \u003cp\u003e2.6.9 Drift detection 45\u003c\/p\u003e \u003cp\u003e2.6.10 Remarks 45\u003c\/p\u003e \u003cp\u003e2.7 Notes 46\u003c\/p\u003e \u003cp\u003eReferences 46\u003c\/p\u003e \u003cp\u003e3 Robust Fault Detection 49\u003c\/p\u003e \u003cp\u003e3.1 Distributed Fault Diagnosis 49\u003c\/p\u003e \u003cp\u003e3.1.1 Introduction 49\u003c\/p\u003e \u003cp\u003e3.1.2 System model 50\u003c\/p\u003e \u003cp\u003e3.1.3 Distributed FDI architecture 55\u003c\/p\u003e \u003cp\u003e3.1.4 Distributed fault detection method 55\u003c\/p\u003e \u003cp\u003e3.1.5 Adaptive thresholds 57\u003c\/p\u003e \u003cp\u003e3.1.6 Distributed fault isolation method 62\u003c\/p\u003e \u003cp\u003e3.1.7 Adaptive thresholds for DFDI 64\u003c\/p\u003e \u003cp\u003e3.1.8 Fault detectability condition 67\u003c\/p\u003e \u003cp\u003e3.1.9 Fault isolability analysis 69\u003c\/p\u003e \u003cp\u003e3.1.10 Stability and learning capability 71\u003c\/p\u003e \u003cp\u003e3.2 Robust Fault Detection Filters 74\u003c\/p\u003e \u003cp\u003e3.2.1 Reference model 74\u003c\/p\u003e \u003cp\u003e3.2.2 Design of adaptive threshold 76\u003c\/p\u003e \u003cp\u003e3.2.3 Iterative update of noise mean and covariance 77\u003c\/p\u003e \u003cp\u003e3.2.4 Unscented transformation (UT) 79\u003c\/p\u003e \u003cp\u003e3.2.5 Car-like mobile robot application 82\u003c\/p\u003e \u003cp\u003e3.3 Simultaneous Fault Detection and Control 90\u003c\/p\u003e \u003cp\u003e3.3.1 Introduction 93\u003c\/p\u003e \u003cp\u003e3.3.2 System model 93\u003c\/p\u003e \u003cp\u003e3.3.3 Problem formulation 95\u003c\/p\u003e \u003cp\u003e3.3.4 Simultaneous fault detection and control problem 96\u003c\/p\u003e \u003cp\u003e3.3.5 Two-tank system simulation 106\u003c\/p\u003e \u003cp\u003e3.4 Data-Driven Fault Detection Design 108\u003c\/p\u003e \u003cp\u003e3.4.1 Introduction 109\u003c\/p\u003e \u003cp\u003e3.4.2 Problem formulation 111\u003c\/p\u003e \u003cp\u003e3.4.3 Selection of weighting matrix 112\u003c\/p\u003e \u003cp\u003e3.4.4 Design of FDF for time-delay system 113\u003c\/p\u003e \u003cp\u003e3.4.5 LMI design approach 114\u003c\/p\u003e \u003cp\u003e3.4.6 Four-tank system simulation 119\u003c\/p\u003e \u003cp\u003e3.5 Robust Adaptive Fault Estimation 122\u003c\/p\u003e \u003cp\u003e3.5.1 Introduction 124\u003c\/p\u003e \u003cp\u003e3.5.2 Problem statement 125\u003c\/p\u003e \u003cp\u003e3.5.3 Adaptive observer 127\u003c\/p\u003e \u003cp\u003e3.6 Notes 131\u003c\/p\u003e \u003cp\u003eReferences 131\u003c\/p\u003e \u003cp\u003e4 Fault-Tolerant Control Systems 135\u003c\/p\u003e \u003cp\u003e4.1 Model Prediction-Based Design Approach 135\u003c\/p\u003e \u003cp\u003e4.1.1 Introduction 135\u003c\/p\u003e \u003cp\u003e4.1.2 System description 136\u003c\/p\u003e \u003cp\u003e4.1.3 Discrete-time UKF 138\u003c\/p\u003e \u003cp\u003e4.1.4 Unscented Transformation (UT) 141\u003c\/p\u003e \u003cp\u003e4.1.5 Controller reconfiguration 143\u003c\/p\u003e \u003cp\u003e4.1.6 Model predictive control 144\u003c\/p\u003e \u003cp\u003e4.1.7 Interconnected CSTR units 149\u003c\/p\u003e \u003cp\u003e4.1.8 Four-tank system 151\u003c\/p\u003e \u003cp\u003e4.1.9 Simulation results 152\u003c\/p\u003e \u003cp\u003e4.1.10 Drift detection in the interconnected CSTRs 152\u003c\/p\u003e \u003cp\u003e4.1.11 Information fusion from UKF 152\u003c\/p\u003e \u003cp\u003e4.1.12 Drift detection in the four-tank system 156\u003c\/p\u003e \u003cp\u003e4.2 Observer-Based Active Structures 160\u003c\/p\u003e \u003cp\u003e4.2.1 Problem statement 160\u003c\/p\u003e \u003cp\u003e4.2.2 A separation principle 162\u003c\/p\u003e \u003cp\u003e4.2.3 FDI residuals 164\u003c\/p\u003e \u003cp\u003e4.2.4 Control of integrity 164\u003c\/p\u003e \u003cp\u003e4.2.5 Overall stability 165\u003c\/p\u003e \u003cp\u003e4.2.6 Design outline 165\u003c\/p\u003e \u003cp\u003e4.2.7 Design of an active FTC scheme 166\u003c\/p\u003e \u003cp\u003e4.2.8 Extraction of FDI–FTC pairs 166\u003c\/p\u003e \u003cp\u003e4.2.9 Simulation 169\u003c\/p\u003e \u003cp\u003e4.3 Notes 172\u003c\/p\u003e \u003cp\u003eReferences 172\u003c\/p\u003e \u003cp\u003e5 Fault-Tolerant Nonlinear Control Systems 175\u003c\/p\u003e \u003cp\u003e5.1 Comparison of Fault Detection Schemes 175\u003c\/p\u003e \u003cp\u003e5.2 Fault Detection in Nonlinear Systems 176\u003c\/p\u003e \u003cp\u003e5.3 Nonlinear Observer-Based Residual Generation Schemes 176\u003c\/p\u003e \u003cp\u003e5.3.1 General considerations 176\u003c\/p\u003e \u003cp\u003e5.3.2 Extended Luenberger observer 177\u003c\/p\u003e \u003cp\u003e5.3.3 Nonlinear identity observer approach 177\u003c\/p\u003e \u003cp\u003e5.3.4 Unknown input observer approach 178\u003c\/p\u003e \u003cp\u003e5.3.5 The disturbance decoupling nonlinear observer approach 178\u003c\/p\u003e \u003cp\u003e5.3.6 Adaptive nonlinear observer approach 178\u003c\/p\u003e \u003cp\u003e5.3.7 High-gain observer approach 178\u003c\/p\u003e \u003cp\u003e5.3.8 Sliding-mode observer approach 178\u003c\/p\u003e \u003cp\u003e5.3.9 Geometric approach 179\u003c\/p\u003e \u003cp\u003e5.3.10 Game-theoretic approach 179\u003c\/p\u003e \u003cp\u003e5.3.11 Observers for Lipschitz nonlinear systems 179\u003c\/p\u003e \u003cp\u003e5.3.12 Lyapunov-reconstruction-based passive scheme 180\u003c\/p\u003e \u003cp\u003e5.3.13 Time-varying results 185\u003c\/p\u003e \u003cp\u003e5.3.14 Optimization-based active scheme 187\u003c\/p\u003e \u003cp\u003e5.3.15 Learning-based active scheme 190\u003c\/p\u003e \u003cp\u003e5.3.16 Adaptive backstepping-based active scheme 191\u003c\/p\u003e \u003cp\u003e5.3.17 Switched control-based active scheme 193\u003c\/p\u003e \u003cp\u003e5.3.18 Predictive control-based active scheme 195\u003c\/p\u003e \u003cp\u003e5.4 Integrated Control Reconfiguration Scheme 197\u003c\/p\u003e \u003cp\u003e5.4.1 Introduction 197\u003c\/p\u003e \u003cp\u003e5.4.2 Basic features 198\u003c\/p\u003e \u003cp\u003e5.4.3 Nonlinear model of a pendulum on a cart 199\u003c\/p\u003e \u003cp\u003e5.4.4 NGA adaptive filter design 201\u003c\/p\u003e \u003cp\u003e5.4.5 Simulation results 207\u003c\/p\u003e \u003cp\u003e5.4.6 Performance evaluation 209\u003c\/p\u003e \u003cp\u003e5.4.7 Comparative studies 211\u003c\/p\u003e \u003cp\u003e5.5 Notes 215\u003c\/p\u003e \u003cp\u003eReferences 215\u003c\/p\u003e \u003cp\u003e6 Robust Fault Estimation 219\u003c\/p\u003e \u003cp\u003e6.1 Introduction 219\u003c\/p\u003e \u003cp\u003e6.2 System Description 220\u003c\/p\u003e \u003cp\u003e6.3 Multiconstrained Fault Estimation 221\u003c\/p\u003e \u003cp\u003e6.3.1 Observer design 221\u003c\/p\u003e \u003cp\u003e6.3.2 Existence conditions 226\u003c\/p\u003e \u003cp\u003e6.3.3 Improved results 228\u003c\/p\u003e \u003cp\u003e6.3.4 Simulation results 232\u003c\/p\u003e \u003cp\u003e6.4 Adaptive Fault Estimation 235\u003c\/p\u003e \u003cp\u003e6.4.1 Introduction 236\u003c\/p\u003e \u003cp\u003e6.4.2 Problem statement 238\u003c\/p\u003e \u003cp\u003e6.4.3 Robust adaptive estimation 239\u003c\/p\u003e \u003cp\u003e6.4.4 Internal stability analysis 240\u003c\/p\u003e \u003cp\u003e6.4.5 Robust performance index 241\u003c\/p\u003e \u003cp\u003e6.4.6 Simulation 242\u003c\/p\u003e \u003cp\u003e6.5 Adaptive Tracking Control Scheme 244\u003c\/p\u003e \u003cp\u003e6.5.1 Attitude dynamics 244\u003c\/p\u003e \u003cp\u003e6.5.2 Fault detection scheme 248\u003c\/p\u003e \u003cp\u003e6.5.3 Fault-tolerant tracking scheme 250\u003c\/p\u003e \u003cp\u003e6.6 Notes 254\u003c\/p\u003e \u003cp\u003eReferences 254\u003c\/p\u003e \u003cp\u003e7 Fault Detection of Networked Control Systems 257\u003c\/p\u003e \u003cp\u003e7.1 Introduction 257\u003c\/p\u003e \u003cp\u003e7.2 Problem Formulation 258\u003c\/p\u003e \u003cp\u003e7.3 Modified Residual Generator Scheme 259\u003c\/p\u003e \u003cp\u003e7.3.1 Modified residual generator and dynamic analysis 259\u003c\/p\u003e \u003cp\u003e7.3.2 Residual evaluation 261\u003c\/p\u003e \u003cp\u003e7.3.3 Co-design of residual generator and evaluation 264\u003c\/p\u003e \u003cp\u003e7.4 Quantized Fault-Tolerant Control 267\u003c\/p\u003e \u003cp\u003e7.4.1 Introduction 267\u003c\/p\u003e \u003cp\u003e7.4.2 Problem statement 268\u003c\/p\u003e \u003cp\u003e7.4.3 Quantized control design 271\u003c\/p\u003e \u003cp\u003e7.4.4 Simulation 276\u003c\/p\u003e \u003cp\u003e7.5 Sliding-Mode Observer 278\u003c\/p\u003e \u003cp\u003e7.5.1 Introduction 278\u003c\/p\u003e \u003cp\u003e7.5.2 Dynamic model 280\u003c\/p\u003e \u003cp\u003e7.5.3 Limited state measurements 286\u003c\/p\u003e \u003cp\u003e7.5.4 Simulation results: full state measurements 290\u003c\/p\u003e \u003cp\u003e7.5.5 Simulation results: partial state measurements 293\u003c\/p\u003e \u003cp\u003e7.6 Control of Linear Switched Systems 294\u003c\/p\u003e \u003cp\u003e7.6.1 Introduction 295\u003c\/p\u003e \u003cp\u003e7.6.2 Problem formulation 295\u003c\/p\u003e \u003cp\u003e7.6.3 Stability of a closed-loop system 296\u003c\/p\u003e \u003cp\u003e7.6.4 Simulation 300\u003c\/p\u003e \u003cp\u003e7.7 Notes 303\u003c\/p\u003e \u003cp\u003eReferences 303\u003c\/p\u003e \u003cp\u003e8 Industrial Fault-Tolerant Architectures 307\u003c\/p\u003e \u003cp\u003e8.1 Introduction 307\u003c\/p\u003e \u003cp\u003e8.2 System Architecture 308\u003c\/p\u003e \u003cp\u003e8.3 Architecture of a Fault-Tolerant Node 309\u003c\/p\u003e \u003cp\u003e8.3.1 Basic architecture 309\u003c\/p\u003e \u003cp\u003e8.3.2 Architecture with improved reliability 310\u003c\/p\u003e \u003cp\u003e8.3.3 Symmetric node architecture 310\u003c\/p\u003e \u003cp\u003e8.3.4 Results 311\u003c\/p\u003e \u003cp\u003e8.4 Recovery Points 312\u003c\/p\u003e \u003cp\u003e8.5 Networks 314\u003c\/p\u003e \u003cp\u003e8.6 System Fault Injection and Monitoring 315\u003c\/p\u003e \u003cp\u003e8.6.1 Monitoring systems 315\u003c\/p\u003e \u003cp\u003e8.6.2 Design methodology 316\u003c\/p\u003e \u003cp\u003e8.7 Notes 318\u003c\/p\u003e \u003cp\u003eReferences 319\u003c\/p\u003e \u003cp\u003e9 Fault Estimation for Stochastic Systems 321\u003c\/p\u003e \u003cp\u003e9.1 Introduction 321\u003c\/p\u003e \u003cp\u003e9.2 Actuator Fault Diagnosis Design 322\u003c\/p\u003e \u003cp\u003e9.3 Fault-Tolerant Controller Design 324\u003c\/p\u003e \u003cp\u003e9.4 Extension to an Unknown Input Case 325\u003c\/p\u003e \u003cp\u003e9.5 Aircraft Application 326\u003c\/p\u003e \u003cp\u003e9.5.1 Transforming the system into standard form 327\u003c\/p\u003e \u003cp\u003e9.5.2 Simulation results 329\u003c\/p\u003e \u003cp\u003e9.6 Router Fault Accommodation in Real Time 330\u003c\/p\u003e \u003cp\u003e9.6.1 Canonical controller and achievable behavior 333\u003c\/p\u003e \u003cp\u003e9.6.2 Router modeling and desired behavior 334\u003c\/p\u003e \u003cp\u003e9.6.3 Description of fault behavior 336\u003c\/p\u003e \u003cp\u003e9.6.4 A least restrictive controller 338\u003c\/p\u003e \u003cp\u003e9.7 Fault Detection for Markov Jump Systems 338\u003c\/p\u003e \u003cp\u003e9.7.1 Introduction 339\u003c\/p\u003e \u003cp\u003e9.7.2 Problem formulation 340\u003c\/p\u003e \u003cp\u003e9.7.3 H∞ bounded real lemmas 343\u003c\/p\u003e \u003cp\u003e9.7.4 H∞ FD filter design 345\u003c\/p\u003e \u003cp\u003e9.7.5 Simulation 347\u003c\/p\u003e \u003cp\u003e9.8 Notes 352\u003c\/p\u003e \u003cp\u003eReferences 353\u003c\/p\u003e \u003cp\u003e10 Applications 355\u003c\/p\u003e \u003cp\u003e10.1 Detection of Abrupt Changes in an Electrocardiogram 355\u003c\/p\u003e \u003cp\u003e10.1.1 Introduction 355\u003c\/p\u003e \u003cp\u003e10.1.2 Modeling ECG signals with an AR model 356\u003c\/p\u003e \u003cp\u003e10.1.3 Linear models with additive abrupt changes 358\u003c\/p\u003e \u003cp\u003e10.1.4 Off-line detection of abrupt changes in ECG 361\u003c\/p\u003e \u003cp\u003e10.1.5 Online detection of abrupt changes in ECG 363\u003c\/p\u003e \u003cp\u003e10.2 Detection of Abrupt Changes in the Frequency Domain 365\u003c\/p\u003e \u003cp\u003e10.2.1 Introduction 365\u003c\/p\u003e \u003cp\u003e10.2.2 Problem formulation 366\u003c\/p\u003e \u003cp\u003e10.2.3 Frequency domain ML ratio estimation 368\u003c\/p\u003e \u003cp\u003e10.2.4 Likelihood of the hypothesis of no abrupt change 372\u003c\/p\u003e \u003cp\u003e10.2.5 Effect of an abrupt change 374\u003c\/p\u003e \u003cp\u003e10.2.6 Simulation results 382\u003c\/p\u003e \u003cp\u003e10.3 Electromechanical Positioning System 383\u003c\/p\u003e \u003cp\u003e10.3.1 Introduction 383\u003c\/p\u003e \u003cp\u003e10.3.2 Problem formulation 385\u003c\/p\u003e \u003cp\u003e10.3.3 Test bed 386\u003c\/p\u003e \u003cp\u003e10.4 Application to Fermentation Processes 387\u003c\/p\u003e \u003cp\u003e10.4.1 Nonlinear faulty dynamic system 388\u003c\/p\u003e \u003cp\u003e10.4.2 Residual characteristics 389\u003c\/p\u003e \u003cp\u003e10.4.3 The parameter filter 399\u003c\/p\u003e \u003cp\u003e10.4.4 Fault filter 400\u003c\/p\u003e \u003cp\u003e10.4.5 Fault isolation and identification 401\u003c\/p\u003e \u003cp\u003e10.4.6 Isolation speed 401\u003c\/p\u003e \u003cp\u003e10.4.7 Parameter partition 402\u003c\/p\u003e \u003cp\u003e10.4.8 Adaptive intervals 402\u003c\/p\u003e \u003cp\u003e10.4.9 Simulation studies 405\u003c\/p\u003e \u003cp\u003e10.5 Flexible-Joint Robots 415\u003c\/p\u003e \u003cp\u003e10.5.1 Problem formulation 415\u003c\/p\u003e \u003cp\u003e10.5.2 Fault detection scheme 417\u003c\/p\u003e \u003cp\u003e10.5.3 Adaptive fault accommodation control 420\u003c\/p\u003e \u003cp\u003e10.5.4 Control with prescribed performance bounds 422\u003c\/p\u003e \u003cp\u003e10.5.5 Simulation results 425\u003c\/p\u003e \u003cp\u003e10.6 Notes 429\u003c\/p\u003e \u003cp\u003eReferences 430\u003c\/p\u003e \u003cp\u003eA Supplementary Information 435\u003c\/p\u003e \u003cp\u003eA.1 Notation 435\u003c\/p\u003e \u003cp\u003eA.1.1 Kronecker products 436\u003c\/p\u003e \u003cp\u003eA.1.2 Some definitions 437\u003c\/p\u003e \u003cp\u003eA.1.3 Matrix lemmas 438\u003c\/p\u003e \u003cp\u003eA.2 Results from Probability Theory 440\u003c\/p\u003e \u003cp\u003eA.2.1 Results-A 440\u003c\/p\u003e \u003cp\u003eA.2.2 Results-B 441\u003c\/p\u003e \u003cp\u003eA.2.3 Results-C 441\u003c\/p\u003e \u003cp\u003eA.2.4 Minimum mean square estimate 442\u003c\/p\u003e \u003cp\u003eA.3 Stability Notions 444\u003c\/p\u003e \u003cp\u003eA.3.1 Practical stabilizability 444\u003c\/p\u003e \u003cp\u003eA.3.2 Razumikhin stability 445\u003c\/p\u003e \u003cp\u003eA.4 Basic Inequalities 447\u003c\/p\u003e \u003cp\u003eA.4.1 Schur complements 447\u003c\/p\u003e \u003cp\u003eA.4.2 Bounding inequalities 449\u003c\/p\u003e \u003cp\u003eA.5 Linear Matrix Inequalities 453\u003c\/p\u003e \u003cp\u003eA.5.1 Basics 453\u003c\/p\u003e \u003cp\u003eA.5.2 Some standard problems 454\u003c\/p\u003e \u003cp\u003eA.5.3 The S-procedure 455\u003c\/p\u003e \u003cp\u003eA.6 Some Formulas on Matrix Inverses 456\u003c\/p\u003e \u003cp\u003eA.6.1 Inverse of block matrices 456\u003c\/p\u003e \u003cp\u003eA.6.2 Matrix inversion lemma 457\u003c\/p\u003e \u003cp\u003eReferences 458\u003c\/p\u003e \u003cp\u003eIndex 459\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406886740311,"sku":"9781118541333","price":103.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118541333.jpg?v=1730497449","url":"https:\/\/bookcurl.com\/products\/analysis-and-synthesis-of-faulttolerant-control-systems-9781118541333","provider":"Book Curl","version":"1.0","type":"link"}