Control of Fractional-Order Systems with Time Delays addresses the widespread problem of uncertainty in the quantifiable parameters of real-world systems. It shows how robust stability and system performance improvements provide essential remedies for the inevitable mismatches between identified models and real-world processes.

The book presents necessary and sufficient conditions for either robust stability analysis or robust stabilization of fractional-order systems for four classes of fractional-order systems as follows:

• systems without delay;
• systems with interval delay;
• Smith-predictor-based control systems; and
• systems with multiple delays.

The book presents proofs that are simple to understand and gives careful consideration to such fundamental control concepts as stability, robust stability analysis, the design of robust controllers, and the improvement of control loop performance. To improve the performance of these systems, the authors put forward two methods: checking the robust D-stability conditions and satisfying the norm constraints. Numerous examples are given to verify the results obtained.

Theoretical results are implemented in the FOMCON (“Fractional-order Modeling and Control”) toolbox for the MATLAB® environment. The book demonstrates the sophistication of the methods it proposes by applying the robust fractional-order controllers it designs to real-world laboratory-scale plants such as servo systems and a twin-rotor aerodynamic system (TRAS).

Control of Fractional-Order Systems with Time Delays will be of most interest to academic researchers working with fractional- and integer-order systems and studying system stability but it will also be of much use to practising engineers working in fields like process, aerospace and automotive control.

Majid Ghorbani received his B.Sc. degree in Control Engineering from Sahand University of Technology, Tabriz, Iran, in 2013, his M.Sc. degree in Control Engineering from K. N. Toosi University of Technology, Tehran, Iran, in 2016, and his Ph.D. degree from Tallinn University of Technology (TalTech), Tallinn, Estonia, in 2025. He is currently a researcher at Tallinn University of Technology (TalTech). His research interests include fractional calculus, data-driven control, time-delay and dead-time systems, robust control, model predictive control, optimization, estimation, and learning-based control methods.

Aleksei Tepljakov received the Ph.D. degree in Information and Communication Technology from Tallinn University of Technology in 2015. Since November 2021, he has held a Senior Research Scientist position at the Department of Computer Systems, School of Information Technologies, Tallinn University of Technology. His main research interests include cyber-physical systems, with a particular focus on fractional-order modeling and control of complex systems. He is also involved in developing efficient mathematical and 3D modeling and interaction methods for virtual and augmented reality, aimed at educational and industrial applications. Among his contributions, he is known for his work on the FOMCON toolbox, which supports research and development in fractional-order control.

Eduard Petlenkov received the PhD degrees in Computer and Systems Engineering from Tallinn University of Technology. He holds the positions of a Tenured Full Professor of Intelligent Control Systems at the Department of Computer Systems, Tallinn University of Technology, and the head of the Centre for Intelligent Systems. His main research interests lie in the domain of nonlinear control, system analysis, computational intelligence, fractional order systems and energy informatics. He is also actively involved in development of intelligent energy efficient control algorithms for commercial buildings.