TY - JOUR
T1 - Generalized Jensen inequalities with application to stability analysis of systems with distributed delays over infinite time-horizons
AU - Liu, Kun
AU - Fridman, Emilia
AU - Johansson, Karl Henrik
AU - Xia, Yuanqing
N1 - Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite delays. In this paper, we first present a generalized integral inequality and its double integral extension. It is shown how these inequalities can be applied to improve the stability result for linear continuous-time systems with gamma-distributed delays. Then, for the discrete-time counterpart we provide an extended Jensen summation inequality with infinite sequences, which leads to less conservative stability conditions for linear discrete-time systems with Poisson-distributed delays. The improvements obtained by the introduced generalized inequalities are demonstrated through examples.
AB - The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite delays. In this paper, we first present a generalized integral inequality and its double integral extension. It is shown how these inequalities can be applied to improve the stability result for linear continuous-time systems with gamma-distributed delays. Then, for the discrete-time counterpart we provide an extended Jensen summation inequality with infinite sequences, which leads to less conservative stability conditions for linear discrete-time systems with Poisson-distributed delays. The improvements obtained by the introduced generalized inequalities are demonstrated through examples.
KW - Gamma-distributed delays
KW - Lyapunov method
KW - New integral and summation inequalities
KW - Poisson-distributed delays
UR - http://www.scopus.com/inward/record.url?scp=84961827087&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2016.02.038
DO - 10.1016/j.automatica.2016.02.038
M3 - Article
AN - SCOPUS:84961827087
SN - 0005-1098
VL - 69
SP - 222
EP - 231
JO - Automatica
JF - Automatica
ER -