Observer-based H control for second-order neutral systems with actuator saturation and the application to mechanical system

  • Lei FuEmail author
  • Yuechao Ma


The observer-based H control problem for second-order neutral systems with actuator saturation is considered. First, a sufficient delay-dependent condition is proposed using Wirtinger-based integral inequality, under which such type neutral system with time-delay and actuator saturation is stable and satisfies H performance. Then, based on the derived condition, the design method of observer-based controller is developed using linear matrix inequalities (LMIs) optimization problem. Finally, a numerical example is provided to illustrate the application of the second-order mechanical systems and the effectiveness of the theoretical results.


Observer-based H control Second-order systems Actuator saturation Linear matrix inequalities (LMIs) 

Mathematics Subject Classification (2010)

93C42 93C73 



  1. Balasubramaniam P, Revathi V, Park J (2013) L2-L∞ filtering for neutral Markovian switching system with mode-dependent time-varying delays and partially unknown transition probabilities. Appl Math Comput 219(17):9524–9542MathSciNetzbMATHGoogle Scholar
  2. Cao Y, Lin Z, Hu T (2002) Stability analysis of linear time-delay systems subjected to input saturation. IEEE Trans Circ Syst 49:233–240zbMATHGoogle Scholar
  3. Chen Y, Fei S, Li Y (2015) Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback. Automatica 52:242–247MathSciNetCrossRefGoogle Scholar
  4. Chen Y, Wang Z, Qian W et al (2017) Memory-based controller design for neutral time-delay systems with input saturations: a novel delay-dependent polytopic approach. J Franklin Inst 354(13):5245–5265MathSciNetCrossRefGoogle Scholar
  5. Dey R, Ghosh S, Ray G, Rakshit A (2014) Improved delay-dependent stabilization of time-delay systems with actuator saturation. Int J Robust Non-linear Control 24(5):902–917MathSciNetCrossRefGoogle Scholar
  6. Dong J, Yang G (2017) Observer-based output feedback control for discrete-time TS fuzzy systems with partly immeasurable premise variables. IEEE Trans Syst Man Cybern Syst 47(1):98–110CrossRefGoogle Scholar
  7. Fang M, Park J (2013) A multiple integral approach to stability of neutral time-delay systems. Appl Math Comput 224:714–718MathSciNetzbMATHGoogle Scholar
  8. Fridman E, Pila A, Shaked U (2003) Regional stabilization and H control of time- delay systems with saturating actuators. Int J Robust Nonlinear Control 13:885–907MathSciNetCrossRefGoogle Scholar
  9. Fu L, Ma Y (2016) Passive control for singular time-delay system with actuator saturation. Appl Math Comput 289:181–193MathSciNetzbMATHGoogle Scholar
  10. Gao J, Su H, Ji X, Chu J (2008) Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity. Nonlinear Anal 9:2350–2360MathSciNetCrossRefGoogle Scholar
  11. Hu T, Lin Z, Chen B (2002) Analysis and design for discrete-time linear systems subject to actuator saturation. Syst Control Lett 45(2):97–112MathSciNetCrossRefGoogle Scholar
  12. Ju H, Kwon O, Lee S (2008) State estimation for neural networks of neutral-type with interval time-varying delays. Appl Math Comput 203(1):217–223MathSciNetzbMATHGoogle Scholar
  13. Lee T, Park J (2017) A novel Lyapunov functional for stability of time-varying delay systems via matrix-refined-function. Automatica 80:239–242MathSciNetCrossRefGoogle Scholar
  14. Lee T, Park J, Xu S (2017) Relaxed conditions for stability of time-varying delay systems. Automatica 75:11–15MathSciNetCrossRefGoogle Scholar
  15. Li N, Ma Z, Wang R et al (2016) Synchronous control of second order linear system based on sliding mode method. Int J Control Autom 9(3):289–298CrossRefGoogle Scholar
  16. Ma Y, Fu L (2016) H robust exponential stability and memory state feedback control for uncertain singular time-delay systems with saturating actuators. IET Control Theory Appl 10(3):328–338MathSciNetCrossRefGoogle Scholar
  17. Ma S, Zhang C (2012) H control for discrete-time singular Markov jump systems subject to actuator saturation. J Franklin Inst 349(3):1011–1029MathSciNetCrossRefGoogle Scholar
  18. Ma Y, Jia X, Liu D (2018) Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates. Appl Math Model 53:49–70MathSciNetCrossRefGoogle Scholar
  19. Mei J, Ren W, Li B et al (2015) Distributed containment control for multiple un- known second-order nonlinear systems with application to networked Lagrangian systems. IEEE Trans Neural Netw Learn Syst 26(9):1885–1899MathSciNetCrossRefGoogle Scholar
  20. Mohajerpoor R, Shanmugam L, Abdi H et al (2016) Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances. J Franklin Inst 354(2):1169–1194MathSciNetCrossRefGoogle Scholar
  21. Ogata K (2009) Modern control engineering, 5th edn. Prentice Hall, LugarzbMATHGoogle Scholar
  22. Qiu F, Cui B, Ji T (2010) Delay-dividing approach for absolute stability of Lurie control system with mixed delays. Nonlinear Anal 11:3110–3120MathSciNetCrossRefGoogle Scholar
  23. Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time- delay systems. Automatica 49:2860–2866MathSciNetCrossRefGoogle Scholar
  24. Shi P, Li F, Wu L et al (2017) Neural network-based passive filtering for delayed neutral- type semi-Markovian jump systems. IEEE Trans Neural Netw Learn Syst 28(9):2101–2114MathSciNetGoogle Scholar
  25. Shokouhi-Nejad H, Rikhtehgar-Ghiasi A (2014) Robust H observer-based controller for stochastic genetic regulatory networks. Math Biosci 250:41–53MathSciNetCrossRefGoogle Scholar
  26. Wang G, Li Z, Zhang Q et al (2017) Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay. Appl Math Comput 293:377–393MathSciNetzbMATHGoogle Scholar
  27. Wen Y, Ren X (2012) Neural observer-based adaptive compensation control for nonlinear time-varying delays systems with input constraints. Expert Syst Appl 39:1944–1955CrossRefGoogle Scholar
  28. Wen G, Chen C, Liu Y et al (2015) Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems. IET Control Theory Appl 9(13):1927–1934MathSciNetCrossRefGoogle Scholar
  29. Yan Y, Yang C, Ma X et al (2018) Sampled-data H filtering for Markovian jump singularly perturbed systems with time-varying delay and missing measurements. Int J Syst Sci 49(3):464–478MathSciNetCrossRefGoogle Scholar
  30. Zhai D, An L, Li J, Zhang Q (2016a) Fault detection for stochastic parameter-varying Markovian jump systems with application to networked control systems. Appl Math Model 40(3):2368–2383MathSciNetCrossRefGoogle Scholar
  31. Zhai D, Lu A, Li J, Zhang Q (2016b) Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time. Appl Math Comput 273:767–792MathSciNetzbMATHGoogle Scholar
  32. Zhang Y, Shi P, Nguang S, Karimi H (2012) Observer-based finite-time fuzzy H control for discrete-time systems with stochastic jumps and time-delays. Signal Processing 97:252–261CrossRefGoogle Scholar

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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of Electrical EngineeringYanshan UniversityQinhuangdaoPeople’s Republic of China
  2. 2.School of ScienceYanshan UniversityQinhuangdaoPeople’s Republic of China

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