Nonlinear Dynamics

, Volume 95, Issue 3, pp 1879–1901 | Cite as

Static anti-windup compensator design for nonlinear time-delay systems subjected to input saturation

  • Muntazir Hussain
  • Muhammad RehanEmail author
  • Choon Ki Ahn
  • Zewei Zheng
Original Paper


In this paper, a novel technique for synthesizing static anti-windup compensator (AWC) is explored for dynamic nonlinear plants with state interval time-delays, exogenous input disturbance, and input saturation nonlinearity, by means of reformulated Lipschitz continuity property. A delay-range-dependent approach, based on Wirtinger-based inequality, is employed to derive a condition for finding the static AWC gain. By using the Lyapunov–Krasovskii functional, reformulated Lipschitz continuity property, Wirtinger-based inequality, sector conditions, bounds on delay, range of time-varying delay, and \(\mathcal {L}_2\) gain reduction, several conditions are derived to guarantee the global and local stabilization of the overall closed-loop system. Further, when the lower time-delay bound is zero, the delay-dependent stabilization condition is derived for saturated nonlinear time-delay systems as a particular scenario of the suggested static AWC design approach. Furthermore, a static AWC design strategy is also provided when a delay-derivative bound is not known. An application to the nonlinear dynamical system is employed to demonstrate the usefulness of the proposed methodologies. A comparative numerical analysis with the existing literature is provided to show the superiority of the proposed AWC results.


Static anti-windup compensator Constrained nonlinear time-delay systems Linear parameter varying (LPV) Reformulated Lipschitz condition \({\mathcal {L}}_2\) gain 



This work was supported in parts by the Higher Education Commission (HEC) of Pakistan through PhD scholarship of the first author (phase II, batch II program) and the National Research Foundation of Korea through the Ministry of Science, ICT and Future Planning under Grant NRF-2017R1A1A1A05001325.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringPakistan Institute of Engineering and Applied Sciences (PIEAS)IslamabadPakistan
  2. 2.School of Electrical EngineeringKorea UniversitySeoulKorea
  3. 3.The Seventh Research Division, School of Automation Science and Electrical EngineeringBeihang UniversityBeijingPeople’s Republic of China

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