Abstract
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.
Highlights
Time delays are usually encountered in numerous industrial systems that must be controlled, such as distributed networks, chemical processes, telecommunications, electrical servo systems, and nuclear reactors, etc. [1,2,3,4]
The problem of developing a nonlinear state-feedback controller was considered for the stabilization of time-delay nonlinear systems subject to structured uncertainties
The mentioned problem was converted into a common optimization problem that was solved in the form of linear matrix inequality (LMI)
Summary
Time delays are usually encountered in numerous industrial systems that must be controlled, such as distributed networks, chemical processes, telecommunications, electrical servo systems, and nuclear reactors, etc. [1,2,3,4]. Studied the robust stabilization problem of a class of time-varying time-delay dynamical systems, which were not perfectly known, where the system output was modeled through a nonlinear function depending on the delayed inputs and states. Two robust H∞ state-feedback controllers based on LMIs for time-delay discrete-time systems and uncertain switched impulsive linear systems were proposed in [28] and [29], respectively. In [30], a robust H∞ fuzzy-logic controller for Takagi–Sugeno time-delay bilinear discrete-time systems in the presence of disturbances was presented in which the stabilization conditions were formulated as LMI. Design of a nonlinear state-feedback stabilizing controller for nonlinear systems in the presence of time delays, Lipschitz nonlinearity, and parametric uncertainties.
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