TY - GEN
T1 - Systems with gamma-distributed delays
T2 - 52nd IEEE Conference on Decision and Control, CDC 2013
AU - Solomon, Oren
AU - Fridman, Emilia
PY - 2013
Y1 - 2013
N2 - In the present paper, sufficient conditions for the exponential stability of linear systems with gamma-distributed delays are presented. Such systems arise in populations dynamics, in traffic flow models, in networked control systems and in other engineering problems. Our main challenge is the stability conditions, where the delay is stabilizing, i.e. the corresponding system with the zero-delay is not asymptotically stable. The results are derived by using augmented Lyapunov functionals, were we generalize the earlier results of [1] and [9], regarding distributed delays and finite constant kernels, to the infinite delay case by extending the corresponding Jensen's integral inequalities and Lyapunov-Krasovskii constructions. Poly topic uncertainties in the system matrices can be easily included in the analysis. Numerical examples illustrate the efficiency of the method. Thus, for the traffic flow model on the ring, where the delay is stabilizing, the resulting stability region almost coincides with the theoretical one found in [11] via the frequency domain analysis.
AB - In the present paper, sufficient conditions for the exponential stability of linear systems with gamma-distributed delays are presented. Such systems arise in populations dynamics, in traffic flow models, in networked control systems and in other engineering problems. Our main challenge is the stability conditions, where the delay is stabilizing, i.e. the corresponding system with the zero-delay is not asymptotically stable. The results are derived by using augmented Lyapunov functionals, were we generalize the earlier results of [1] and [9], regarding distributed delays and finite constant kernels, to the infinite delay case by extending the corresponding Jensen's integral inequalities and Lyapunov-Krasovskii constructions. Poly topic uncertainties in the system matrices can be easily included in the analysis. Numerical examples illustrate the efficiency of the method. Thus, for the traffic flow model on the ring, where the delay is stabilizing, the resulting stability region almost coincides with the theoretical one found in [11] via the frequency domain analysis.
KW - Consensus
KW - Gamma-distributed delay
KW - Lyapunov-Krasovskii method
KW - Stabilization by delay
UR - http://www.scopus.com/inward/record.url?scp=84902336628&partnerID=8YFLogxK
U2 - 10.1109/CDC.2013.6759901
DO - 10.1109/CDC.2013.6759901
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AN - SCOPUS:84902336628
SN - 9781467357173
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 318
EP - 323
BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 10 December 2013 through 13 December 2013
ER -