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

  • Saleh MobayenEmail author
  • Gisela Pujol-Vázquez
Research Paper


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.


Nonlinear feedback stabilization Linear matrix inequalities Lipschitz nonlinearity Lyapunov–Krasovskii functional Time-delay 



This work was partially supported by the Spanish Ministry of Economy, Industry and Competitiveness, under grants DPI2016-77407-P (AEI/FEDER, UE).


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of ZanjanZanjanIran
  2. 2.Department of MathematicsUniversitat Politècnica de CatalunyaTerrassaSpain

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