“By combining finite time control and sliding mode control with time-synchronized control, the book develops a new ‘time-synchronized stability’ definition. This work is helpful for theoretical researchers, engineers, and students who dedicate themselves to creating the best control system design in practice yet with sound theoretical knowledge. … These unique natures and properties make time-synchronized control highly attractive … .” (Dongya Zhao, Mathematical Reviews, January, 2023)
“This book includes some of the authors’ previous works that are published in some top journals. It can be served as a good textbook for researchers, engineers and graduates who dedicate themselves for the best control system design in practice.” (Peijun Wang, zbMATH 1493.93001, 2022)
Previous research on fixed/finite-time sliding-mode control focuses on forcing a system state (vector) to converge within a certain time moment, regardless of how each state element converges. This book introduces a control problem with unique finite/fixed-time stability considerations, namely time-synchronized stability, where at the same time, all the system state elements converge to the origin, and fixed-time-synchronized stability, where the upper bound of the synchronized settling time is invariant with any initial state. Accordingly, sufficient conditions for (fixed-) time-synchronized stability are presented. These stability formulations grant essentially advantageous performance when a control system (with diversified subsystems) is expected to accomplish multiple actions synchronously, e. g., grasping with a robotic hand, multi-agent simultaneous cooperation, etc. Further, the analytical solution of a (fixed) time-synchronized stable system is obtained and discussed. Applications to linear systems, disturbed nonlinear systems, and network systems are provided. In addition, comparisons with traditional fixed/finite-time sliding mode control are suitably detailed to showcase the full power of (fixed-) time-synchronized control.
