TY - JOUR
T1 - Stability of singularly perturbed differential-difference systems
T2 - A LMI approach
AU - Fridman, E.
PY - 2002/6
Y1 - 2002/6
N2 - For linear singularly perturbed system with delay sufficient conditions for stability for all small enough values of singular perturbation parameter ε are obtained in the general case, when delay and ε are independent. The sufficient delay-dependent conditions are given in terms of linear matrix inequalities (LMIs) by applying an appropriate Lyapunov-Krasovskii functional. LMIs are derived by using a descriptor model transformation and Park's inequality for bounding cross terms. A memoryless state-feedback stabilizing controller is obtained. Solution is given also in the case of systems with polytopic parameter uncertainties. Numerical examples illustrate the effectiveness of the new theory.
AB - For linear singularly perturbed system with delay sufficient conditions for stability for all small enough values of singular perturbation parameter ε are obtained in the general case, when delay and ε are independent. The sufficient delay-dependent conditions are given in terms of linear matrix inequalities (LMIs) by applying an appropriate Lyapunov-Krasovskii functional. LMIs are derived by using a descriptor model transformation and Park's inequality for bounding cross terms. A memoryless state-feedback stabilizing controller is obtained. Solution is given also in the case of systems with polytopic parameter uncertainties. Numerical examples illustrate the effectiveness of the new theory.
KW - Delay-dependent criteria
KW - LMI
KW - Singular perturbations
KW - Stability
KW - Time-delay systems
UR - http://www.scopus.com/inward/record.url?scp=0347935782&partnerID=8YFLogxK
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AN - SCOPUS:0347935782
SN - 1492-8760
VL - 9
SP - 201
EP - 212
JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
IS - 2
ER -