Singular systems, also referred to as implicit systems, descriptor systems, or generalized state-space systems, have drawn considerable attention. As a generalization of standard state-space description, singular systems are widely applied to engineering systems, biological systems, and economic systems. They provide more precise descriptions of dynamic systems, as they may contain impulsive elements and non-dynamic constraints.
Singular systems whose states represent quantities that are intrinsically nonnegative, for example, volumes of liquids, number of molecules, and species population, are called positive singular systems. Such system has a nonnegative state and output as long as the initial condition and the input are nonnegative. With standard positive systems being an active field of research, increasing attention is paid to the study of positive singular systems.
In our work, an auxiliary system is introduced to establish the positivity condition for singular time-delay systems. Based on the positivity condition, the stability criterion is obtained for the singular systems with constant delays. By analyzing the monotonic property of the system trajectory, we extend the stability condition to the cases with time-varying delays.
Cui Yukang received his B.S. in Automation from the Harbin Institute of Technology in July, 2012. He received his Ph.D. in Mechanical Engineering from the University of Hong Kong in Match, 2017. Then, he served as a research associate in the University of Hong Kong from April to June, 2017.
He has been serving as reviewer for journals like, Mechatronics, IET Control Theory & Applications, Part I: Journal of Systems and Control Engineering, Advances in Mechanical Engineering, IMA Journal of Mathematical Control and Information, IEEE Transactions on Neural Networks and Learning Systems. His research interests include singular time-delay systems, positive systems, and nonlinear systems.