Recent Progress in Stability and Stabilization of Systems with Time-Delays

Abstract

This paper overviews the research investigations pertaining to stability and stabilization of control systems with time-delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay-independent and delay-dependent stability results for time-delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay-dependent stability results are also discussed.

Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays

“…Since the sixteen's century, the research theme of time-delay systems has concerned lots of interest and has been considered as one of the essential research areas in control theory for which many significant research works have been devoted. The topical survey [9] and the recent books [10][11][12] as well as their related references prove the richness and maturity of this field. Time delays can appear in either the state variables, control inputs, or measurement outputs and the negligence of time delays in the controller design can lead to undesirable dynamics such as oscillations, bifurcations, chaos dynamics, and instability [8].…”

Repetitive control design for switched neutral systems with input time‐delay

“…However, it is noted that the standard controllers struggle to regulate real-world processes with time-delays. [10][11][12][13][14][15][16][17] Most of the existing works in dynamical systems does not focus on delay compensator-based control with input time delays. [18][19][20] For eliminating the effect of time delay, the Smith predictor is a common delay compensating system that incorporates both a compensator and a predictor.…”