TY - JOUR
T1 - Disturbance attenuation properties of time-controlled switched systems
AU - Zhai, Guisheng
AU - Hu, Bo
AU - Yasuda, Kazunori
AU - Michel, Anthony N.
N1 - Funding Information:
In the proof of Theorem 1 , we have referred the techniques proposed in Dr. Hespanha's contributions [7,14] . This work is supported in part by Japanese Society for the Promotion of Science under the Grant-in-Aid for Encouragement of Young Scientists 11750396, and in part by an Alexander von Humboldt Foundation Senior Research Award, Institut für Nachrichtentechnik, Ruhr-Universität Bochum, Germany.
PY - 2001/11
Y1 - 2001/11
N2 - In this paper, we investigate the disturbance attenuation properties of time-controlled switched systems consisting of several linear time-invariant subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than a positive scalar γ0, the switched system under an average dwell time scheme achieves a weighted disturbance attenuation level γ0, and the weighted disturbance attenuation approaches normal disturbance attenuation if the average dwell time is chosen sufficiently large. We extend this result to the case where not all subsystems are Hurwitz stable, by showing that in addition to the average dwell time scheme, if the total activation time of unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, then a reasonable weighted disturbance attenuation level is guaranteed. Finally, a discussion is made on the case for which nonlinear norm-bounded perturbations exist in the subsystems.
AB - In this paper, we investigate the disturbance attenuation properties of time-controlled switched systems consisting of several linear time-invariant subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than a positive scalar γ0, the switched system under an average dwell time scheme achieves a weighted disturbance attenuation level γ0, and the weighted disturbance attenuation approaches normal disturbance attenuation if the average dwell time is chosen sufficiently large. We extend this result to the case where not all subsystems are Hurwitz stable, by showing that in addition to the average dwell time scheme, if the total activation time of unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, then a reasonable weighted disturbance attenuation level is guaranteed. Finally, a discussion is made on the case for which nonlinear norm-bounded perturbations exist in the subsystems.
KW - Average dwell time
KW - Disturbance attenuation
KW - Perturbations
KW - Piecewise Lyapunov function
KW - Switched system
KW - Switching law
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U2 - 10.1016/S0016-0032(01)00030-8
DO - 10.1016/S0016-0032(01)00030-8
M3 - Article
AN - SCOPUS:0035498653
SN - 0016-0032
VL - 338
SP - 765
EP - 779
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 7
ER -