1 Motivating Examples 1.1 Switched Systems 1.1.1 Supervisory Switching Control 1.1.2 Switched Server System 1.1.3 Singular System with Markov Switching 1.2 Impulsive Systems 1.2.1 SEIRS Epidemic Model with Impulse Vaccinations 1.2.2 Insulin Treatment References 2 Mathematical Background 2.1 Basic Definitions 2.2 Comparison Method 2.3 Delay Systems 2.4 Impulsive Systems 2.5 Comparison Method for Impulsive Systems 2.6 Impulsive Systems with Time Delay 2.7 Stochastic Differential Equations 2.7.1 Notations and Basic Definitions 2.7.2 Stochastic Processes 2.7.3 Stochastic Differential Equations 2.7.4 Comparison Method for Stochastic Systems 2.8 Stochastic Impulsive System with Time Delay 2.9 Switched Systems 2.9.1 System Formulation 2.9.2 Systems with Stable Subsystems 2.10 Stochastic Switched Systems with Time Delay 2.11 Singularly Perturbed Systems 2.12 Miscellaneous Results 2.13 Notes and Comments References 3 Fundamental Properties of Stochastic Impulsive Systems with Time Delay 3.1 Existence of Solution 3.2 Forward Continuation 3.3 Global Existence 3.4 Uniqueness of Solution 3.5 Notes and Comments References 4 Stability of Stochastic Impulsive Systems with Time Delay 4.1 Stability Analysis by Classical Lyapunov Technique 4.2 Stability Analysis by Comparison Method 4.3 Notes and Comments References 5 Large-Scale Stochastic Impulsive Systems with Time Delay 5.1 Problem Formulation 5.2 Analysis by Lyapunov Method 5.3 Comparison Method 5.3.1 Method of Lyapunov Function 5.3.2 Method of Vector Lyapunov Functions 5.4 Examples 5.5 Notes and Comments References 6 Input-to-State Stability for Stochastic Switched Systems 6.1 Problem Formulation 6.2 Initial-State-Dependent Dwell-Time 6.3 Markovian Switching 6.4 Notes and Comments References 7 Reliable Control for Stochastic Switched Systems with State Delay 7.1 Problem Formulation 7.2 Stability Analysis 7.3 Numerical Example 7.4 Notes and Comments References 8 Robust Reliable Control for Impulsive Large-Scale Systems 8.1 Problem Formulation 8.2 Reliable Control 8.3 State Estimation 8.4 Notes and Comments References 9 Switched Singularly Perturbed Systems with Time Delay 9.1 Problem Formulation 9.2 Stability Analysis 9.2.1 Linear Systems 9.2.2 Nonlinear Systems 9.3 Notes and Comments References 10 Singularly Perturbed Impulsive-Switched Systems with Time Delay 10.1 Problem Formulation 10.2 Stability Analysis 10.2.1 Linear Systems 10.2.2 Nonlinear Systems 10.3 Notes and Comments Reference 11 Stabilization and State Estimation via Sliding Mode Control 11.1 Problem Formulation 11.2 Slow Sliding Mode Control Design 11.2.1 Sliding Mode Control with Multiple Inputs 11.2.2 Reachability Analysis 11.3 Sliding Mode Luenberger Observer 11.4 Numerical Examples 11.5 Notes and Comments References 12 Comparison Method and Stability of EPCA 12.1 Introduction 12.2 Problem Formulation 12.3 Comparison Method 12.4 Stability Analysis 12.5 Numerical Examples 12.6 Application 12.7 Notes and Comments References 13 Existence, Uniqueness and Stability of Stochastic EPCA 13.1 Existence and Uniqueness of Solutions 13.2 Comparison Method 13.3 Stability Analysis 13.4 Notes and Comments References
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