I have worked for many years with many researchers on the stability properties of delay systems. Moreover, I was very much interested in the stabilization of systems with input delays and in the use of delays for the construction of feedback laws that can guarantee special properties to the corresponding closed-loop system.
Results for delay systems are included in the following book chapters:
I. Karafyllis and P. Pepe, “A Note on Converse Lyapunov Results for Neutral Systems”, Recent Results on Nonlinear Time Delayed Systems, I. Karafyllis, M. Malisoff, F. Mazenc and P. Pepe (Eds.), Advances in Delays and Dynamics, Vol. 4, Springer, 2015.
T. Ahmed-Ali, I. Karafyllis, M. Krstic and F. Lamnabhi-Lagarrigue, “Robust Stabilization of Nonlinear Globally Lipschitz Delay Systems”, Recent Results on Nonlinear Time Delayed Systems, I. Karafyllis, M. Malisoff, F. Mazenc and P. Pepe (Eds.), Advances in Delays and Dynamics, Vol. 4, Springer, 2015.
I. Karafyllis, M. Malisoff, F. Mazenc, and P. Pepe, “Stabilization of Nonlinear Delay Systems: A Tutorial on Recent Results”, Recent Results on Nonlinear Time Delayed Systems, I. Karafyllis, M. Malisoff, F. Mazenc and P. Pepe (Eds.), Advances in Delays and Dynamics, Vol. 4, Springer, 2015.
I. Karafyllis and M. Krstic, “Sampled-Data Stabilization of Nonlinear Delay Systems with a Compact Absorbing Set and State Measurement”, Time Delay Systems, Theory, Numerics, Applications, and Experiments, T. Insperger, T. Ersal and G. Orosz (Eds.), Advances in Delays and Dynamics, Vol. 7, Springer, 2017.
Results for delay systems are included in the following journal papers:
I. Karafyllis, “Lyapunov Theorems for Systems Described by Retarded Functional Differential Equations”, Nonlinear Analysis: Theory, Methods and Applications, 64(3), 2006, pp. 590-617.
I. Karafyllis, “Finite-Time Global Stabilization by Means of Time-Varying Distributed Delay Feedback”, SIAM Journal Control and Optimization, 45(1), 2006, pp. 320-342.
P. Pepe, I. Karafyllis and Z.-P. Jiang, “On the Liapunov-Krasovskii Methodology for the ISS of Systems described by Coupled Delay Differential and Difference Equations”, Automatica, 44(9), 2008, pp. 2266-2273.
I. Karafyllis, “Global Stabilization by Means of Discrete-Delay Static Output Feedback”, Systems & Control Letters, 57(12), 2008, pp. 987-995.
I. Karafyllis, P. Pepe and Z.-P. Jiang, “Global Output Stability for Systems Described by Retarded Functional Differential Equations: Lyapunov Characterizations”, European Journal of Control, 14(6), 2008, pp. 516-536.
I. Karafyllis, P. Pepe and Z.-P. Jiang, “Input-to-Output Stability for Systems Described by Retarded Functional Differential Equations”, European Journal of Control, 14(6), 2008, pp. 539-555.
I. Karafyllis, P. Pepe and Z.-P. Jiang, “Stability Results for Systems Described by Coupled Retarded Functional Differential Equations and Functional Difference Equations”, Nonlinear Analysis, Theory, Methods and Applications, 71(7-8), 2009, pp. 3339-3362.
I. Karafyllis and Z.-P. Jiang, “Stability and Control of Nonlinear Systems Described by Retarded Functional Equations: A Review of Recent Results”, Science in China Series F: Information Sciences, 52(11), 2009, pp. 2104-2126.
I. Karafyllis and Z.-P. Jiang, “Necessary and Sufficient Lyapunov-like Conditions for Robust Nonlinear Stabilization”, ESAIM Control, Optimisation and Calculus of Variations, 16(4), 2010, pp. 887-928.
I. Karafyllis, “Stabilization By Means of Approximate Predictors for Systems with Delayed Input”, SIAM Journal on Control and Optimization, 49(3), 2011, pp. 1100-1123.
I. Karafyllis and M. Krstic, “Nonlinear Stabilization under Sampled and Delayed Measurements, and with Inputs Subject to Delay and Zero-Order Hold”, IEEE Transactions on Automatic Control, 57(5), 2012, pp. 1141-1154.
P. Pepe and I. Karafyllis, “Converse Lyapunov-Krasovskii Theorems for Systems Described by Neutral Functional Differential Equations in Hale’s Form”, International Journal of Control, 86(2), 2013, pp. 232-243.
I. Karafyllis and M. Krstic, “Delay-Robustness of Linear Predictor Feedback Without Restriction on Delay Rate”, Automatica, 49(6), 2013, pp. 1761-1767.
I. Karafyllis and M. Krstic, “Stabilization of Nonlinear Delay Systems Using Approximate Predictors and High-Gain Observers”, Automatica, 49(12), 2013, pp. 3623–3631.
I. Karafyllis, M. Krstic, T. Ahmed-Ali and F. Lamnabhi-Lagarrigue, “Global Stabilization of Nonlinear Delay Systems with a Compact Absorbing Set”, International Journal of Control, 87(5), 2014, pp. 1010-1027.
I. Karafyllis and M. Krstic, “On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations”, ESAIM Control, Optimisation and Calculus of Variations, 20(3), 2014, pp. 894 - 923.
I. Karafyllis and M. Krstic, “Numerical Schemes for Nonlinear Predictor Feedback”, Mathematics of Control, Signals, and Systems, 26(4), 2014, pp. 519-546.
I. Karafyllis, M. Malisoff, M. de Queiroz, M. Krstic and R. Yang, “Predictor-Based Tracking for Neuromuscular Electrical Stimulation”, International Journal of Robust and Nonlinear Control, 25(14), 2015, pp. 2391-2419.
I. Karafyllis and M. Krstic, “Sampled-Data Stabilization of Nonlinear Delay Systems with a Compact Absorbing Set”, SIAM Journal on Control and Optimization, 54(2), 2016, pp. 790–818.
P. Pepe, I. Karafyllis and Z.-P. Jiang, “Lyapunov-Krasovskii Characterization of the Input-to-State Stability for Neutral Systems in Hale’s Form”, Systems & Control Letters, 102, 2017, pp. 48-56.
I. Karafyllis and M. Krstic, “Stability of Integral Delay Equations and Stabilization of Age-Structured Models”, ESAIM Control, Optimisation and Calculus of Variations, 23(4), 2017, pp. 1667-1714.
X. Li, R. Wang, I. Karafyllis, X.-M. Sun, “L2-gain Analysis for Systems with Interval Time-Varying Delay based on the Switching Technique”, Journal of the Franklin Institute, 354(17), 2017, pp. 7968-7982.
T. Ahmed-Ali, I. Karafyllis and F. Giri, “Sampled-Data Observers for Delay Systems and Hyperbolic PDE-ODE Loops”, Automatica, 123, 2021, 109349.
I. Karafyllis and A. Chaillet, “Lyapunov Conditions for Uniform Asymptotic Output Stability and a Relaxation of Barbălat’s Lemma”, Automatica, 132, 2021, 109792.
I. Karafyllis, P. Pepe, A. Chaillet and Y. Wang, “Is Global Asymptotic Stability Necessarily Uniform for Time-Delay Systems?”, SIAM Journal on Control and Optimization, 60(6), 2022, pp. 3237-3261.
A. Chaillet, I. Karafyllis, P. Pepe and Y. Wang, “The ISS Framework for Time-Delay systems: A Survey”, Mathematics of Control, Signals, and Systems, 35, 2023, pp. 237–306.
A. Chaillet, I. Karafyllis, P. Pepe and Y. Wang, “Growth Conditions for Global Exponential Stability and exp-ISS of Time-Delay Systems Under Point-Wise Dissipation”, Systems & Control Letters, 178, 2023, 105570.
I. Karafyllis, M. Krstic and A. Aslanidis, “On Disturbance-to-State Adaptive Stabilization without Parameter Bound by Nonlinear Feedback of Delayed State and Input”, SIAM Journal on Control and Optimization, 61(6), 2023, pp. 3584-3607.
E. Loko, A. Chaillet and I. Karafyllis, “Building Coercive Lyapunov-Krasovskii Functionals Based on Razumikhin and Halanay Approaches”, International Journal of Robust and Nonlinear Control, 34(10), 2024, pp. 6372-6392.
Finally, results for delay systems are included in the following books:
I. Karafyllis and Z.-P. Jiang, Stability and Stabilization of Nonlinear Systems, Springer-Verlag, London (Series: Communications and Control Engineering), 2011.
I. Karafyllis and M. Krstic, Predictor Feedback for Delay Systems: Implementations and Approximations, Birkhäuser, Boston (Series: Mathematics, Systems & Control: Foundations & Applications), 2017.