An LMI Approach to Nonlinear State-Feedback Stability of Uncertain Time-Delay Systems in the Presence of Lipschitzian Nonlinearities

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.

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

“…To evaluate the performance of the proposed approach, we applied it to a ball and beam system and compared the obtained dynamics to that of the system proposed in [1]. In a ball and beam configuration, the objective is typically to balance a ball in an unstable equilibrium position.…”

“…This is further exacerbated when disturbances are added to the system. To date, various approaches have been developed and implemented to control and/or stabilize nonlinear disturbed systems [1][2][3][4][5]. Because system states are affected by disturbances and nonlinearities, errors emerge in dynamical systems, and disregarding their impact, may lead to extreme deterioration in system performance and even instability [6][7][8].…”

Dynamic Population on Bio-Inspired Algorithms Using Machine Learning for Global Optimization

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“…The optimization landscape has been further enriched by the development of adaptive algorithms that fluidly transition between global and local search strategies, offering more effective exploration and exploitation of the solution space [ 3 ]. These adaptive methodologies have shown great promise in managing the variability and complexity of contemporary systems, finding applications in as diverse fields as logistics, energy system management, and the design of cutting-edge materials [ 23 , 24 , 29 , 39 ].…”

“…The convergence of optimization and machine learning continues to be a fertile area for research and development, heralding an era of intelligent optimization solutions that are not only faster and more efficient but also capable of adapting to an array of complex challenges [ 29 , 44 , 45 ]. These solutions are set to redefine the future of decision making and system analysis, providing innovative responses to the dynamic and ever-evolving environments of the modern world [ 25 , 30 , 37 , 39 , 43 ].…”