An LMI approach to nonlinear state-feedback stability of uncertain time-delay systems in the presence of lipschitzian nonlinearities

An LMI approach to nonlinear state-feedback stability of uncertain time-delay systems in the presence of lipschitzian nonlinearities

Golestani, Mehdi (Iran University of Science and Technology)
Mobayen, Saleh (National Yunlin University of Science and Technology)
Hassan HosseinNia, S. (TU Delft Mechatronic Systems Design)
Shamaghdari, Saeed (Iran University of Science and Technology)

2020

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.

Linear matrix inequality
Lipschitz nonlinearity
Parametric uncertainty
State-feedback stabilization
Time delays

http://resolver.tudelft.nl/uuid:533b314e-5d9c-4c51-9ded-5d008074e141

https://doi.org/10.3390/sym12111883

Symmetry, 12 (11)

Institutional Repository

journal article

© 2020 Mehdi Golestani, Saleh Mobayen, S. Hassan HosseinNia , Saeed Shamaghdari