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Preface; Contents; 1 Sampled-Data Stabilization of Nonlinear Delay Systems with a Compact Absorbing Set and State Measurement; Abstract; 1 Introduction; 2 Problem Description and Main Result; 3 Proof of Main Result; Appendix: Proof of Lemma 3.3; References; Parametric Transfer Matrices for Sampled-Data Control Systems with Linear Continuous Periodic Process and Control Delay; 1 Introduction; 2 Mathematical Description of LCP Processes; 3 PTM of Open SD System with LCP Process and Delay; 4 PTM of Closed SD System with LCP Process and Delay
3.1 New Sufficient Conditions for Lyapunov and BIBO Stability4 The Observation Problem; 5 Time-Varying Delay; 5.1 Backward Selection; 5.2 Forwarding; 5.3 State Dependent Delay; 6 Conclusions; References; A New Delay-Independent Stability Test for LTI Systems with Single Delay; 1 Introduction; 2 Preliminaries; 2.1 Kronecker Sum and Delay-Independent Stability; 2.2 Bistritz Tabulation Method; 3 Main Results; 4 Case Studies; 5 Conclusion; References; Numerical Stability Test of Linear Time-Delay Systems of Neutral Type; 1 Introduction; 2 The Location of the Characteristic Roots of DDEs
3 Stability Test of NDDEs3.1 Stability Criteria; 3.2 Numerical Test; 3.3 Illustrative Examples; 4 Calculation of the Rightmost Characteristic Root; 5 Conclusions; References; Utilizing Topological Data Analysis for Studying Signals of Time-Delay Systems; 1 Introduction; 2 Background; 2.1 Takens Embedding; 2.2 Persistent Homology; 2.3 Maximum Persistence; 3 Stochastic Model Equations; 3.1 Scalar Autonomous SDDE: Stochastic Hayes Equation; 3.2 Time-Periodic SDDE: Stochastic Mathieu Equation; 4 Results; 4.1 Numerical Simulation; 4.2 Persistence Computation; 4.3 Stocahstic Hayes Equation Results
4.4 Stochastic Mathieu Equation Results5 Discussion; References; Stability and Control of Fractional Periodic Time-Delayed Systems; 1 Introduction; 2 Caputo Fractional Derivative; 3 Transition Curves Using Explicit Harmonic Balance Method; 3.1 Formulation; 3.2 Example: Fractional Damped Delayed Mathieu Equation; 4 Stability and Control Using the Fractional Chebyshev Collocation Method; 4.1 Fractional Chebyshev Differentiation Matrix; 4.2 Fractional Chebyshev Collocation Method; 4.3 Example: Stability of the Fractional Hayes Equation
3.1 New Sufficient Conditions for Lyapunov and BIBO Stability4 The Observation Problem; 5 Time-Varying Delay; 5.1 Backward Selection; 5.2 Forwarding; 5.3 State Dependent Delay; 6 Conclusions; References; A New Delay-Independent Stability Test for LTI Systems with Single Delay; 1 Introduction; 2 Preliminaries; 2.1 Kronecker Sum and Delay-Independent Stability; 2.2 Bistritz Tabulation Method; 3 Main Results; 4 Case Studies; 5 Conclusion; References; Numerical Stability Test of Linear Time-Delay Systems of Neutral Type; 1 Introduction; 2 The Location of the Characteristic Roots of DDEs
3 Stability Test of NDDEs3.1 Stability Criteria; 3.2 Numerical Test; 3.3 Illustrative Examples; 4 Calculation of the Rightmost Characteristic Root; 5 Conclusions; References; Utilizing Topological Data Analysis for Studying Signals of Time-Delay Systems; 1 Introduction; 2 Background; 2.1 Takens Embedding; 2.2 Persistent Homology; 2.3 Maximum Persistence; 3 Stochastic Model Equations; 3.1 Scalar Autonomous SDDE: Stochastic Hayes Equation; 3.2 Time-Periodic SDDE: Stochastic Mathieu Equation; 4 Results; 4.1 Numerical Simulation; 4.2 Persistence Computation; 4.3 Stocahstic Hayes Equation Results
4.4 Stochastic Mathieu Equation Results5 Discussion; References; Stability and Control of Fractional Periodic Time-Delayed Systems; 1 Introduction; 2 Caputo Fractional Derivative; 3 Transition Curves Using Explicit Harmonic Balance Method; 3.1 Formulation; 3.2 Example: Fractional Damped Delayed Mathieu Equation; 4 Stability and Control Using the Fractional Chebyshev Collocation Method; 4.1 Fractional Chebyshev Differentiation Matrix; 4.2 Fractional Chebyshev Collocation Method; 4.3 Example: Stability of the Fractional Hayes Equation