TY - JOUR
T1 - Constructive Robust Stabilization by Using Square Wave Dithers
T2 - A Time-Delay Approach
AU - Zhang, Jin
AU - Fridman, Emilia
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2023/10/1
Y1 - 2023/10/1
N2 - This article studies robust stabilization of the second- and third-order (with relative degree 3) linear uncertain systems by a fast-varying square wave dither with high frequency 1/ϵ and high gain, where ϵ >0 is small. In contrast to the existing methods for control by fast oscillations that are all qualitative, we present constructive quantitative results for finding an upper bound on ϵ that ensures the exponential stability. Our method consists of two steps: 1) we construct appropriate coordinate transformations that cancel the high gains and lead to a stable averaged system; 2) we apply the time-delay approach to periodic averaging of the system in new coordinates and derive linear matrix inequalities for finding an upper bound on ϵ. Three numerical examples illustrate the efficiency of the method.
AB - This article studies robust stabilization of the second- and third-order (with relative degree 3) linear uncertain systems by a fast-varying square wave dither with high frequency 1/ϵ and high gain, where ϵ >0 is small. In contrast to the existing methods for control by fast oscillations that are all qualitative, we present constructive quantitative results for finding an upper bound on ϵ that ensures the exponential stability. Our method consists of two steps: 1) we construct appropriate coordinate transformations that cancel the high gains and lead to a stable averaged system; 2) we apply the time-delay approach to periodic averaging of the system in new coordinates and derive linear matrix inequalities for finding an upper bound on ϵ. Three numerical examples illustrate the efficiency of the method.
KW - Averaging
KW - stabilization by fast oscillations
KW - time-delay systems
UR - http://www.scopus.com/inward/record.url?scp=85146253054&partnerID=8YFLogxK
U2 - 10.1109/TAC.2022.3230772
DO - 10.1109/TAC.2022.3230772
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AN - SCOPUS:85146253054
SN - 0018-9286
VL - 68
SP - 6307
EP - 6314
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 10
ER -