TY - JOUR
T1 - Probability-guaranteed robust H∞ performance analysis and state-feedback design
AU - Yaesh, I.
AU - Boyarski, S.
AU - Shaked, U.
PY - 2003/4/15
Y1 - 2003/4/15
N2 - This paper addresses the common engineering practice of specifying a required probability of attaining some performance level. The problem setup is that of a robust H∞ performance analysis/state-feedback synthesis of an affinely parameter-dependent linear system, except that the parameter hyper-rectangle (box) is allowed to shrink - representing a probability less than one - in order to accommodate a polytopic performance goal that is better than the one attainable for the original parameter box. A new version of the bounded real lemma (BRL), which assigns a different Lyapunov function to each of the vertices of the uncertainty polytope and includes a scalar-free parameter, seems to reduce the overdesign associated with the polytopic problem to the bare minimum. The shrinking of the parameter box leads to bi-linear matrix inequalities (BLMIs), since the final vertices are also unknown. These BLMIs are solved iteratively; three steps have sufficed, both in the analysis and in the state-feedback design examples. A uniform distribution is assumed for all the system parameters, following the uniformity principle. The probability requirement is expressed by a set of linear matrix inequalities (LMIs) that is derived by extending an existing second-order cone method; these LMIs are concurrently solved with the BLMIs of the BRL. The features of the proposed method are demonstrated via two examples.
AB - This paper addresses the common engineering practice of specifying a required probability of attaining some performance level. The problem setup is that of a robust H∞ performance analysis/state-feedback synthesis of an affinely parameter-dependent linear system, except that the parameter hyper-rectangle (box) is allowed to shrink - representing a probability less than one - in order to accommodate a polytopic performance goal that is better than the one attainable for the original parameter box. A new version of the bounded real lemma (BRL), which assigns a different Lyapunov function to each of the vertices of the uncertainty polytope and includes a scalar-free parameter, seems to reduce the overdesign associated with the polytopic problem to the bare minimum. The shrinking of the parameter box leads to bi-linear matrix inequalities (BLMIs), since the final vertices are also unknown. These BLMIs are solved iteratively; three steps have sufficed, both in the analysis and in the state-feedback design examples. A uniform distribution is assumed for all the system parameters, following the uniformity principle. The probability requirement is expressed by a set of linear matrix inequalities (LMIs) that is derived by extending an existing second-order cone method; these LMIs are concurrently solved with the BLMIs of the BRL. The features of the proposed method are demonstrated via two examples.
KW - H-infinity optimization
KW - Probabilistic performance
KW - Robustness
KW - State-feedback design
UR - http://www.scopus.com/inward/record.url?scp=0037445802&partnerID=8YFLogxK
U2 - 10.1016/S0167-6911(02)00289-X
DO - 10.1016/S0167-6911(02)00289-X
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AN - SCOPUS:0037445802
SN - 0167-6911
VL - 48
SP - 351
EP - 364
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 5
ER -