TY - JOUR
T1 - H∞ control of linear singularly perturbed systems with small state delay
AU - Glizer, Valery Y.
AU - Fridman, Emilia
PY - 2000/10/1
Y1 - 2000/10/1
N2 - An infinite horizon H∞ state-feedback control problem for singularly perturbed linear systems with a small state delay is considered. An asymptotic solution of the hybrid system of Riccati-type algebraic, ordinary differential, and partial differential equations with deviating arguments, associated with this problem, is constructed. Based on this asymptotic solution, conditions for the existence of a solution of the original H∞ problem, independent of the singular perturbation parameter, are derived. A simplified controller with parameter-independent gain matrices, solving the original problem for all sufficiently small values of this parameter, is obtained. An illustrative example is presented.
AB - An infinite horizon H∞ state-feedback control problem for singularly perturbed linear systems with a small state delay is considered. An asymptotic solution of the hybrid system of Riccati-type algebraic, ordinary differential, and partial differential equations with deviating arguments, associated with this problem, is constructed. Based on this asymptotic solution, conditions for the existence of a solution of the original H∞ problem, independent of the singular perturbation parameter, are derived. A simplified controller with parameter-independent gain matrices, solving the original problem for all sufficiently small values of this parameter, is obtained. An illustrative example is presented.
UR - http://www.scopus.com/inward/record.url?scp=0034288413&partnerID=8YFLogxK
U2 - 10.1006/jmaa.2000.6955
DO - 10.1006/jmaa.2000.6955
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AN - SCOPUS:0034288413
SN - 0022-247X
VL - 250
SP - 49
EP - 85
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -