Transformations from Variable Delays to Constant Delays with Applications in Engineering and Biology

Abstract

This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike. 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. 5 PTM of System mathcalSτ as Function of the Argument λ6 Numerical Example; 7 Conclusions; References; An SL/QP Algorithm for Minimizing the Spectral Abscissa of Time Delay Systems; 1 Introduction; 2 Algorithms for Eigenvalue Optimization; 2.1 State of the Art; 2.2 Sequential Linear and Quadratic Methods; 3 Numerical Results; 4 Conclusion; References; The Principle of ``Borrowed Feedback'' and Application to Control and Observation for Systems with Implicit State Dependent Delay; 1 Introduction; 2 The Control Problem; 2.1 Measure of Goodness; 3 Stability of the Closed Loop.