TY - JOUR
T1 - An LMI approach to nonlinear state-feedback stability of uncertain time-delay systems in the presence of lipschitzian nonlinearities
AU - Golestani, Mehdi
AU - Mobayen, Saleh
AU - Hosseinnia, S. Hassan
AU - Shamaghdari, Saeed
PY - 2020
Y1 - 2020
N2 - This article proposes a new nonlinear state-feedback stability controller utilizing linear matrix inequality (LMI) for time-delay nonlinear systems in the presence of Lipschitz nonlinearities and subject to parametric uncertainties. Following the Lyapunov–Krasovskii stabilization scheme, the asymptotic stability criterion resulted in the LMI form and the nonlinear state-feedback control technique was determined. Due to their significant contributions to the system stability, time delays and system uncertainties were taken into account while the suggested scheme was designed so that the system’s stabilization was satisfied in spite of time delays and system uncertainties. The benefit of the proposed method is that not only is the control scheme independent of the system order, but it is also fairly simple. Hence, there is no complexity in using the proposed technique. Finally, to justify the proficiency and performance of the suggested technique, a numerical system and a rotational inverted pendulum were studied. Numerical simulations and experimental achievements prove the efficiency of the suggested control technique.
AB - This article proposes a new nonlinear state-feedback stability controller utilizing linear matrix inequality (LMI) for time-delay nonlinear systems in the presence of Lipschitz nonlinearities and subject to parametric uncertainties. Following the Lyapunov–Krasovskii stabilization scheme, the asymptotic stability criterion resulted in the LMI form and the nonlinear state-feedback control technique was determined. Due to their significant contributions to the system stability, time delays and system uncertainties were taken into account while the suggested scheme was designed so that the system’s stabilization was satisfied in spite of time delays and system uncertainties. The benefit of the proposed method is that not only is the control scheme independent of the system order, but it is also fairly simple. Hence, there is no complexity in using the proposed technique. Finally, to justify the proficiency and performance of the suggested technique, a numerical system and a rotational inverted pendulum were studied. Numerical simulations and experimental achievements prove the efficiency of the suggested control technique.
KW - Linear matrix inequality
KW - Lipschitz nonlinearity
KW - Parametric uncertainty
KW - State-feedback stabilization
KW - Time delays
UR - http://www.scopus.com/inward/record.url?scp=85096536843&partnerID=8YFLogxK
U2 - 10.3390/sym12111883
DO - 10.3390/sym12111883
M3 - Article
AN - SCOPUS:85096536843
VL - 12
JO - Symmetry
JF - Symmetry
IS - 11
M1 - 1883
ER -