Circuits, Systems, and Signal Processing

, Volume 38, Issue 12, pp 5467–5487 | Cite as

Finite-Time Stabilization of Descriptor Time-Delay Systems with One-Sided Lipschitz Nonlinearities: Application to Partial Element Equivalent Circuit

  • Maryam Sadat AsadiniaEmail author
  • Tahereh BinazadehEmail author


This paper deals with the design of a stabilizing state feedback controller for a class of nonlinear time-delay descriptor system over the finite-time interval. The considered system is exposed to parameter uncertainties and time-varying disturbances. To provide a wider and more general class of nonlinear time-delay descriptor systems, the nonlinear parts of the system are assumed to be a function of state variables, delayed state variables, input and also delayed input and to satisfy the one-sided Lipschitz condition. The purpose of finite-time control is to propose a robust control law such that the resulting closed-loop system is stable, impulse free and regular for all admissible model uncertainties over the considered time interval. Additionally, the designed controller ensures the \( H_{\infty } \) disturbance attenuation of the closed-loop descriptor system. In order to achieve these goals, two theorems are given. The sufficient conditions are gained based on the delay-dependent analyses. These conditions then are converted to solvable linear matrix inequalities (LMIs). Finally, simulations are provided a practical example, to confirm the theoretical achievements. The practical example is a partial element equivalent circuit which is a neutral time-delay system. This system is transformed into a time-delay descriptor system. Simulation outcomes illustrate the effective performance of the given method in robust finite-time stabilization.


One-sided Lipschitz Delay-dependent analysis Time-delay descriptor systems Finite-time interval \( H_{\infty } \) disturbance attenuation Partial element equivalent circuit 



  1. 1.
    S. Ahmad, M. Rehan, On observer-based control of one-sided Lipschitz systems. J. Franklin Inst. 353(4), 903–916 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    M.S. Asadinia, T. Binazadeh, B. Safarinejadian, A delay-range-dependent stabilization of uncertain singular time-delay systems with one-sided Lipschitz nonlinearities subject to input saturation. J. Vibr. Control 25(4), 868–881 (2019)MathSciNetCrossRefGoogle Scholar
  3. 3.
    M.S. Asadinia, T. Binazadeh, Design of robust control law for stabilization of singular systems with time-varying delay in the presence of model uncertainty and input amplitude constraint. J. Control 10(3), 14–27 (2016)Google Scholar
  4. 4.
    M.S. Asadinia, T. Binazadeh, Robust soft variable structure control of perturbed singular systems with constrained input. Control Cybern. 46(4), 345–360 (2017)MathSciNetzbMATHGoogle Scholar
  5. 5.
    M.S. Asadinia, T. Binazadeh, Stabilization of time varying delay singular systems subject to actuator saturation. Tabriz J. Electr. Eng. 47(3), 843–855 (2017)Google Scholar
  6. 6.
    Z. Belhadi, A. Bérard, H. Mohrbach, Faddeev-Jackiw quantization of non-autonomous singular systems. Phys. Lett. A 380(41), 3355–3358 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    J. Cullum, A. Ruehli, T. Zhang, A method for reduced-order modeling and simulation of large interconnect circuits and its application to PEEC models with retardation. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 47(4), 261–273 (2000)CrossRefGoogle Scholar
  8. 8.
    A. Dastaviz, T. Binazadeh, Simultaneous stabilization for a collection of uncertain time-delay systems using sliding-mode output feedback control. Int. J. Control (2018).
  9. 9.
    M. Ekramian, M. Ataei, S. Talebi, Stability of nonlinear time-delay systems satisfying a quadratic constraint. Trans. Inst. Meas. Control 40(3), 712–718 (2018)CrossRefGoogle Scholar
  10. 10.
    E. Fridman Introduction to Time-Delay Systems: Analysis and Control. In: Systems and Control: Foundations and Applications. Springer, Birkhäuser, 2014Google Scholar
  11. 11.
    L. Gao, Y. Cui, W. Chen, Leader-following consensus for discrete-time descriptor multi-agent systems with observer-based protocols. Trans. Inst. Meas. Control 38(11), 1353–1364 (2016)CrossRefGoogle Scholar
  12. 12.
    H. Gholami, T. Binazadeh, Robust finite-time H controller design for uncertain one-sided Lipschitz systems with time-delay and input amplitude constraints. Circuit Syst. Signal Process. (2019).
  13. 13.
    H. Gholami, T. Binazadeh, Sliding-mode observer design and finite-time control of one-sided Lipschitz nonlinear systems with time-delay, Soft Comput. (2018)
  14. 14.
    K. Gu, An integral inequality in the stability problem of time-delay systems. in Proc. 39th IEEE Conf. Decision Control, 2000, 2805–2810Google Scholar
  15. 15.
    S. He, J. Song, F. Liu, Robust finite-time bounded controller design of time-delay conic nonlinear systems using sliding mode control strategy, IEEE Trans. Syst. Man Cybern. Syst.
  16. 16.
    S. He, Q. Ai, Ch. Ren, J. Dong, F. Liu, Finite-time resilient controller design of a class of uncertain nonlinear systems with time-delays under asynchronous switching, IEEE Trans. Syst. Man Cybern. Syst.
  17. 17.
    Y. Huang, S. Fu, Y. Shen, Finite-time H control for one-sided Lipschitz systems with auxiliary matrices. Neurocomputing 124, 205–215 (2016)Google Scholar
  18. 18.
    J.Y. Ishihara, M.H. Terra, On the Lyapunov theorem for singular systems. IEEE Trans. Autom. Control 47, 1926–1930 (2002)MathSciNetCrossRefGoogle Scholar
  19. 19.
    E. Jafari, T. Binazadeh, Modified composite nonlinear feedback control for output tracking of nonstep signals in singular systems with actuator saturation. Int. J. Robust Nonlinear Control 28(16), 4885–4899 (2018)MathSciNetCrossRefGoogle Scholar
  20. 20.
    E. Jafari, T. Binazadeh, Modified composite nonlinear feedback for nonstep output tracking of multi-input multi-output linear discrete-time singular systems with actuator saturation, in 2017 5th International Conference on Control, Instrumentation, and Automation (ICCIA), pp. 114–119. IEEE, 2017Google Scholar
  21. 21.
    E. Jafari, T. Binazadeh, Observer-based improved composite nonlinear feedback control for output tracking of time-varying references in descriptor systems with actuator saturation, ISA Transaction (2019).
  22. 22.
    E. Jafari, T. Binazadeh, Robust output regulation in discrete-time singular systems with actuator saturation and uncertainties. IEEE Trans. Circuits Syst. II Express Briefs (2019).
  23. 23.
    N. Jiang, X. Liu, J. Cao, A unified framework for finite-time and fixed-time stabilization of neural networks with general activations and external disturbances. Circuits Syst. Signal Process. 38(3), 1005–1022 (2019)CrossRefGoogle Scholar
  24. 24.
    S. Kririm, A. Hmamed, F. Tadeo, Analysis and design of H∞ controllers for 2D singular systems with delays. Circuits Syst. Signal Process. 35(5), 1579–1592 (2016)CrossRefGoogle Scholar
  25. 25.
    J. Li, Q. Zhang, X.G. Yan, S.K. Spurgeon, Observer-based fuzzy integral sliding mode control for nonlinear descriptor systems. IEEE Trans. Fuzzy Syst. 26(5), 2818–2832 (2018)CrossRefGoogle Scholar
  26. 26.
    X. Lin, K. Liang, H. Li, Y. Jiao, J. Nie, Finite-time stability and stabilization for continuous systems with additive time-varying delays. Circuits Syst. Signal Process. 36(7), 2971–2990 (2017)CrossRefGoogle Scholar
  27. 27.
    Z. Liu, L. Zhao, H. Xiao, C. Gao, Adaptive H integral sliding mode control for uncertain singular time-delay systems based on observer. Circuits Syst. Signal Process. 36(11), 4365–4387 (2017)MathSciNetCrossRefGoogle Scholar
  28. 28.
    J. Liu, T. Zhang, L. Zhao, B. Liu, X. Wei, Analysis and control of the singular system model of aphid ecosystems,
  29. 29.
    H. Liu, X. Zhao, Finite-time H control of switched systems with mode dependent averaged well time. J. Frankl. Inst. 351, 1301–1315 (2014)CrossRefGoogle Scholar
  30. 30.
    G. Liu, Y. Wei, Q. Ma, J. Lu, Y. Chu, Robust non-fragile guaranteed cost control for singular Markovian jump time-delay systems. Trans. Inst. Meas. Control 40(7), 2141–2150 (2018)CrossRefGoogle Scholar
  31. 31.
    Y. Ma, L. Fu, Robust H control for singular time-delay systems with saturating actuators via static output feedback. Comput. Appl. Math. 37(2), 2260–2276 (2018)MathSciNetCrossRefGoogle Scholar
  32. 32.
    P. Niamsup, V.N. Phat, A new result on finite-time control of singular linear time-delay systems. Appl. Math. Lett. 60, 1–7 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    J. Ooi, ChP Tan, S.G. Nurzaman, K.Y. Ng, A sliding mode observer for infinitely unobservable descriptor systems. IEEE Trans. Autom. Control 62(7), 3580–3587 (2017)MathSciNetCrossRefGoogle Scholar
  34. 34.
    S. Sekar, M. Vijayarakavan, Observer design of singular systems (Robot arm model) using leapfrog method. Glob. J. Pure Appl. Math. 11(1), 68–71 (2015)Google Scholar
  35. 35.
    R.J. Shi, Patton, fault estimation and active fault tolerant control for linear parameter varying descriptor systems. Int. J. Robust Nonlinear Control Banner 25(5), 689–706 (2015)CrossRefGoogle Scholar
  36. 36.
    J. Song, S. He, Robust finite-time H control for one-sided Lipschitz nonlinear systems via state feedback and output feedback. J. Franklin Inst. 352(8), 3250–3266 (2015)MathSciNetCrossRefGoogle Scholar
  37. 37.
    J. Song, Y. Niu, Y. Zou, Finite-time stabilization via sliding mode control. IEEE Trans. Autom. Control 62(3), 1478–1483 (2017)MathSciNetCrossRefGoogle Scholar
  38. 38.
    M. Su, S.W. Wang, X. Zhang, Finite-time stability for singular linear time-delay systems with time-varying exogenous disturbance. Adv. Mater. Res. 490–495, 2459–2463 (2012)CrossRefGoogle Scholar
  39. 39.
    J. Tian, J. Wang, Sh. Ma, Observer design for one-sided Lipschitz nonlinear continuous-time singular systems with unknown input, in Control and Decision Conference, 2016, (Chinese) Google Scholar
  40. 40.
    J. Wang, S. Maa, C. Zhang, Resilient estimation for T-S fuzzy descriptor systems with semi-Markov jumps and time-varying delay. Inf. Sci. 430–431, 104–126 (2018)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Y. Wang, Y. Xia, H. Shen, P. Zhou, SMC design for robust stabilization of nonlinear Markovian jump singular systems. IEEE Trans. Autom. Control 63(1), 219–224 (2018)MathSciNetCrossRefGoogle Scholar
  42. 42.
    H. Wanga, A. Xuec, R. Luc, Absolute stability criteria for a class of nonlinear singular systems with time delay. Nonlinear Anal. 70, 621–630 (2009)MathSciNetCrossRefGoogle Scholar
  43. 43.
    S. Xu, J. Lu, S.H. Zhou, C.H. Yang, Design of observers for a class of discrete-time uncertain nonlinear systems with time-delay. J. Franklin Inst. 341(3), 225–302 (2004)MathSciNetCrossRefGoogle Scholar
  44. 44.
    X. Yang, X. Lia, J. Cao, Robust finite-time stability of singular nonlinear systems with interval time-varying delay. J. Franklin Inst. 355(3), 1241–1258 (2018)MathSciNetCrossRefGoogle Scholar
  45. 45.
    A. Zemouche, R. Rajamani, H. Kheloufi, F. Bedouhene, Robust observer-based stabilization of Lipschitz nonlinear uncertain systems via LMIs—discussions and new design procedure. Int. J. Robust Nonlinear Control Banner 27(11), 1915–1939 (2017)MathSciNetCrossRefGoogle Scholar
  46. 46.
    H.B. Zeng, Y. He, M. Wu, J. She, Free-matrix-based integral inequality for stability analysis of systems with time-varying delay. IEEE Trans. Autom. Control 60(10), 2768–2772 (2015)MathSciNetCrossRefGoogle Scholar
  47. 47.
    W. Zhang, H. Su, F. Zhu, S.P. Bhattacharyya, Improved exponential observer design for one-sided Lipschitz nonlinear systems. Int. J. Robust Nonlinear Control 26(18), 3958–3973 (2016)MathSciNetCrossRefGoogle Scholar
  48. 48.
    W. Zhang, H. Su, H. Wang, Z. Han, Full-order and reduced-order observers for one-sided Lipschitz nonlinear systems using Riccati equations. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4968–4977 (2012)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Z. Zhao, F. Lv, J. Zhang, Y. Du, H synchronization for uncertain time-delay Chaotic systems with one-sided Lipschitz nonlinearity. IEEE Access 6, 19798–19806 (2018)CrossRefGoogle Scholar
  50. 50.
    Z. Zuo, J. Zhang, Y. Wang, Adaptive fault-tolerant tracking control for linear and Lipschitz nonlinear multi-agent systems. IEEE Trans. Ind. Electron. 62(6), 3923–3931 (2015)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringShiraz University of TechnologyShirazIran

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