TY - JOUR
T1 - Wirtinger's inequality and Lyapunov-based sampled-data stabilization
AU - Liu, Kun
AU - Fridman, Emilia
N1 - Funding Information:
This work was partially supported by Israel Science Foundation (grant No 754/10 ), and by China Scholarship Council . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen.
PY - 2012/1
Y1 - 2012/1
N2 - Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.
AB - Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.
KW - LMI
KW - LyapunovKrasovskii functional
KW - Sampled-data systems
KW - Time-delay
UR - http://www.scopus.com/inward/record.url?scp=84355161690&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2011.09.029
DO - 10.1016/j.automatica.2011.09.029
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AN - SCOPUS:84355161690
SN - 0005-1098
VL - 48
SP - 102
EP - 108
JO - Automatica
JF - Automatica
IS - 1
ER -