A Robust LMI Approach on Nonlinear Feedback Stabilization of Continuous State-Delay Systems with Lipschitzian Nonlinearities: Experimental Validation

This paper suggests a novel nonlinear state-feedback stabilization control law using linear matrix inequalities for a class of time-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov–Krasovskii stability theory, the asymptotic stabilization criterion is d...

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Vydané v:Iranian journal of science and technology. Transactions of mechanical engineering Ročník 43; číslo 3; s. 549 - 558
Hlavní autori: Mobayen, Saleh, Pujol-Vázquez, Gisela
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.09.2019
Predmet:
Engineering
Mechanical Engineering
Research Paper
Lipschitz nonlinearity
Nonlinear feedback stabilization
Time-delay
Linear matrix inequalities
Lyapunov–Krasovskii functional
ISSN:2228-6187, 2364-1835
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Popis
Shrnutí:This paper suggests a novel nonlinear state-feedback stabilization control law using linear matrix inequalities for a class of time-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov–Krasovskii stability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coefficients of the nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to find the proper feedback gain matrix  F is also provided. The robustness purpose against nonlinear functions and time delays is guaranteed in this scheme. Moreover, the problem of robust H ∞ performance analysis for a class of nonlinear time-delayed systems with external disturbance is studied in this paper. Simulations are presented to demonstrate the proficiency of the offered technique. For this purpose, an unstable nonlinear numerical system and a rotary inverted pendulum system have been studied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendulum system is provided. These results confirm the expected satisfactory performance of the suggested method.
ISSN:2228-6187
2364-1835
DOI:10.1007/s40997-018-0223-4