TY - GEN
T1 - Stability analysis of discrete time delay control for nonlinear systems
AU - Jung, Je Hyung
AU - Chang, Pyung Hun
AU - Kang, Sang Hoon
PY - 2007
Y1 - 2007
N2 - This paper presents a solution to the long standing problem of the stability of Time Delay Control (TDC) for nonlinear systems. Ever since it was first introduced, TDC has rapidly drawn attentions owing to its unusually robust performance and yet its extraordinarily compact form. The existing stability analyses have been made based on the assumption that the TDC is continuous and time delay L → 0. The assumption, however, not only fails to reflect the reality that TDC is usually implemented in a digital processor, but also leads to a stability criterion in which important parameters, such as L, that play crucial roles are absent. In this paper, therefore, we present our theoretical investigation on the stability of TDC with the premise that TDC is discrete and L is nonzero and finite. Specifically, stability criteria based on the premise are derived, so that one may clearly grasp which parameters affect stability and how. For the analysis of the closed-loop stability, we have first derived its approximate discrete model (approximate discrete plant model with the discrete TDC). Then by using the model and the concepts of consistency and Lyapunov stability, we have analyzed the stability of the exact discrete model of closed loop systems. The analysis results in a stability criteria consisting of L and other parameters that affect the performance of TDC. The suggested stability analysis has been verified by simulation results.
AB - This paper presents a solution to the long standing problem of the stability of Time Delay Control (TDC) for nonlinear systems. Ever since it was first introduced, TDC has rapidly drawn attentions owing to its unusually robust performance and yet its extraordinarily compact form. The existing stability analyses have been made based on the assumption that the TDC is continuous and time delay L → 0. The assumption, however, not only fails to reflect the reality that TDC is usually implemented in a digital processor, but also leads to a stability criterion in which important parameters, such as L, that play crucial roles are absent. In this paper, therefore, we present our theoretical investigation on the stability of TDC with the premise that TDC is discrete and L is nonzero and finite. Specifically, stability criteria based on the premise are derived, so that one may clearly grasp which parameters affect stability and how. For the analysis of the closed-loop stability, we have first derived its approximate discrete model (approximate discrete plant model with the discrete TDC). Then by using the model and the concepts of consistency and Lyapunov stability, we have analyzed the stability of the exact discrete model of closed loop systems. The analysis results in a stability criteria consisting of L and other parameters that affect the performance of TDC. The suggested stability analysis has been verified by simulation results.
UR - https://www.scopus.com/pages/publications/46449090913
U2 - 10.1109/ACC.2007.4282317
DO - 10.1109/ACC.2007.4282317
M3 - Conference contribution
AN - SCOPUS:46449090913
SN - 1424409888
SN - 9781424409884
T3 - Proceedings of the American Control Conference
SP - 5995
EP - 6002
BT - Proceedings of the 2007 American Control Conference, ACC
T2 - 2007 American Control Conference, ACC
Y2 - 9 July 2007 through 13 July 2007
ER -