Recent Advances in Theory and Practice of Time-Delay Systems Analysis and Control

Dear Colleagues,

One can find a large number of systems and processes exhibiting various forms of delay or non-simultaneous action of various quantities all around. This phenomenon applies not only in technical practice but also in a wide range of non-technical human activities, e.g., in biology or economics, and can be reflected in the relevant mathematical models. In some cases, latency can be observed only in the input–output relationship (e.g., in material transport). However, the delaying effect on the feedback between the output and the input is often an inherent part of the system or its model (e.g., in looped heating–cooling networks). In addition, the delay can have different forms—it can act in one place or, conversely, be spatially distributed. It is a well-known fact that the delay in the feedback—whether as part of the (controlled) system or process itself or in a closed control loop—can have a negative effect on the dynamic properties of the system, especially on its stability. In the latter case, the existence of shifted arguments in the left (output) side of the differential equation in models of systems with delay, the so-called delay-differential equations, makes analysis and control design disproportionately more difficult than in the case of non-delayed systems, due to their infinite-dimensional nature.

The study of the influence of delays on system stability, dynamics, and control performance poses a challenging mathematical exercise. Current theory is confronted with increasing requirements for the quality and performance of control systems in the industry and everyday practice, which can hardly be achieved using conventional methods. In order to meet these goals, more in-depth knowledge of the controlled delayed systems is a prerequisite. Despite significant advances in artificial intelligence techniques and strategies in recent years, distinguished scholars still find innovative solutions to the existing task and define new open problems that stem from an ever more profound understanding of this reign.

This Special Issue of Mathematics is focused on recent developments in approaches and solutions to time-delay dynamical systems analysis and control design. The goal was to attract quality and novel papers in the field of “Theory and Practice of Time-Delay Systems Analysis and Control”. Besides purely theoretical research results, applications from diverse fields of human activity are welcome.

This Special Issue of Mathematics is focused on recent developments in approaches to time-delay systems analysis and control design. We seek papers on system stability and dynamics analysis, including exponential, asymptotic, strong, delay-dependent, delay-independent, BIBO, H2, H_∞, polynomial, global, and other types of system stability. Results on asymptotic and long-time behavior, synchronization; Hopf, fold, and pitchfork bifurcation; stability switching; dynamic mode decomposition, eigenvalue analyses, and properties of the evolution operator are also welcome. Special consideration will be given to delays of neutral types and systems given by algebraic-differential equations; however, systems with retarded delays are also acceptable due to their practicability. In addition, the scope of this Special Issue includes modern control methods and their applications, such as switched systems, event-triggered control, Lyapunov–Razumikhin- and Krasovskii-type approaches, etc. Following recent advances in artificial intelligence, modeling, identification, and control strategies based on machine learning principles, such as reinforcement learning, deep learning, bidirectional associative memory, and convolutional neural networks, can be considered as well.

All submitted papers will be peer-reviewed and selected based on their quality and relevance to this Special Issue.

Dr. Libor Pekař
Prof. Dr. Mengjie Song
Dr. Radek Matušů
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• time-invariant and time-variant delayed systems
• delay-varying models and their stability
• linear and nonlinear delayed systems
• dynamics and stability of systems with retarded and neutral delays
• delayed systems described by algebraic-differential equations
• exponential, asymptotic, strong, delay-dependent, delay-independent, BIBO, H2, H∞, and polynomial stability of time-delay systems
• delay-dependent and delay-independent stability
• hopf, fold, and pitchfork bifurcation, stability switching
• dynamic mode decomposition, eigenvalue analyses, properties of the evolution operator
• semi-discretization and full-discretization methods
• finite-dimension approximations
• filtering and estimation of time-delay systems
• switched systems with time delay and event-triggered control
• Krasovskii-type and Lyapunov–Razumikhin-type stability and control approaches
• new results in controllability and observability of time-delay systems
• robust, algebraic, and adaptive control methods and their applications
• machine learning principles, reinforcement learning, deep learning in modeling and control
• bidirectional associative memory and convolutional neural networks
• laboratory and experimental verification
• real-life applications in the reign of time-delay systems

• Advances in Study of Time-Delay Systems and Their Applications, 2nd Edition in Mathematics (9 articles)