Research Papers

Robust Tracking Control of a Class of Switched Nonlinear Systems With Input Delay Under Asynchronous Switching

[+] Author and Article Information
Saeed Pezeshki

Faculty of Electrical and Computer Engineering,
University of Tabriz,
Tabriz 5166616471, Iran
e-mail: saeedpezeshki@tabrizu.ac.ir

Mohammad Ali Badamchizadeh

Faculty of Electrical and Computer Engineering,
University of Tabriz,
Tabriz 5166616471, Iran
e-mail: mbadamchi@tabrizu.ac.ir

Amir Rikhtehgar Ghiasi

Faculty of Electrical and Computer Engineering,
University of Tabriz,
Tabriz 5166616471, Iran
e-mail: agiasi@tabrizu.ac.ir

Sehraneh Ghaemi

Faculty of Electrical and Computer Engineering,
University of Tabriz,
Tabriz 5166616471, Iran
e-mail: ghaemi@tabrizu.ac.ir

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 6, 2017; final manuscript received November 10, 2017; published online December 22, 2017. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 140(6), 061013 (Dec 22, 2017) (11 pages) Paper No: DS-17-1240; doi: 10.1115/1.4038491 History: Received May 06, 2017; Revised November 10, 2017

This paper concerns the problems of stability and robust model reference tracking control for a class of switched nonlinear systems with input delay under asynchronous switching. By proposing a new Lyapunov–Krasovskii functional, and using free-weighting matrices and average dwell-time (ADT) technique, new input-to-state stability (ISS) conditions are derived in terms of linear matrix inequalities (LMIs) under a certain delay bound. Then, robust model reference tracking control problem is studied based on the proposed Lyapunov–Krasovskii functional; Finally a kind of state feedback control law which guarantees robust model reference tracking performance is proposed. Illustrative examples are presented to demonstrate the efficacy and feasibility of results.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Dong, C. Y. , Li, W. , and Wang, Q. , 2013, “ H∞ Control of Switched Systems With Nonideal Switchings and Its Application to Morphing Aircraft,” Procedia Eng., 67, pp. 100–109. [CrossRef]
Huang, R. , Zhang, J. , and Zhang, X. , 2016, “ Adaptive Tracking Control of Uncertain Switched Nonlinear Systems With Application to Aircraft Wing Rock,” IET Control Theory Appl., 10(15), pp. 1755–1762. [CrossRef]
Chen, S. , Jiang, L. , Yao, W. , and Wu, Q. H. , 2014, “ Application of Switched System Theory in Power System Stability,” 49th International Universities Power Engineering Conference (UPEC), Cluj-Napoca, Romania, Sept. 2–5, pp. 1–6.
Zong, G. D. , Ren, H. L. , and Hou, L. L. , 2016, “ Finite-Time Stability of Interconnected Impulsive Switched Systems,” IET Control Theory Appl., 10(6), pp. 648–654. [CrossRef]
Lin, H. , and Antsaklis, P. J. , 2009, “ Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results,” IEEE Trans. Autom. Control, 54(2), pp. 308–322. [CrossRef]
Hespanha, J. P. S. , and Morse, A. , 2002, “ Switching Between Stabilizing Controllers,” Automatica, 38(11), pp. 1905–1917. [CrossRef]
Ma, R. , and Zhao, J. , 2010, “ Backstepping Design for Global Stabilization of Switched Nonlinear Systems in Lower Triangular Form Under Arbitrary Switchings,” Automatica, 46(11), pp. 1819–1823. [CrossRef]
Aleksandrov, A. Y. , Chen, Y. , Platonov, A. V. , and Zhang, L. , 2011, “ Stability Analysis for a Class of Switched Nonlinear Systems,” Automatica, 47(10), pp. 2286–2291. [CrossRef]
Zhao, X. , Zhang, L. , Shi, P. , and Liu, M. , 2012, “ Stability of Switched Positive Linear Systems With Average Dwell Time Switching,” Automatica, 48(6), pp. 1132–1137. [CrossRef]
Zhang, J. , Han, Z. , Zhu, F. , and Zhao, X. , 2014, “ Absolute Exponential Stability and Stabilization of Switched Nonlinear Systems,” Syst. Control Lett., 66, pp. 51–57. [CrossRef]
Mahmoud, M. S. , 2010, Switched Time-Delay Systems: Stability and Control, Springer Press, Boston, MA. [CrossRef]
Liu, J. , Liu, X. Z. , and Xie, W. C. , 2008, “ Delay-Dependent Robust Control for Uncertain Switched Systems With Time-Delay,” Nonlinear Anal.: Hybrid Syst., 2(1), pp. 81–95. [CrossRef]
Zamani, I. , Shafiee, M. , and Ibeas, A. , 2013, “ Exponential Stability of Hybrid Switched Nonlinear Singular Systems With Time-Varying Delay,” J. Franklin Inst., 350(1), pp. 171–193. [CrossRef]
Wang, X. H. , Zong, G. D. , and Sun, H. , 2016, “ Asynchronous Finite-Time Dynamic Output Feedback Control for Switched Time-Delay Systems With Non-Linear Disturbances,” IET Control Theory Appl., 10(10), pp. 1142–1150. [CrossRef]
Liu, H. , Shen, Y. , and Zhao, X. , 2013, “ Asynchronous Finite-Time H∞ Control for Switched Linear Systems Via Mode-Dependent Dynamic State-Feedback,” Nonlinear Anal.: Hybrid Syst., 8, pp. 109–120. [CrossRef]
Ma, D. , and Zhao, J. , 2015, “ Stabilization of Networked Switched Linear Systems: An Asynchronous Switching Delay System Approach,” Syst. Control Lett., 77, pp. 46–54. [CrossRef]
Wang, Y. E. , Wu, B. W. , and Wu, C. , 2017, “ Stability and L2-Gain Analysis of Switched Input Delay Systems With Unstable Modes Under Asynchronous Switching,” J. Franklin Inst., 354(11), pp. 4481–4497. [CrossRef]
Li, Q. K. , Zhao, J. , Liu, X. J. , and Dimirovski, G. M. , 2011, “ Observer-Based Tracking Control for Switched Linear Systems With Time-Varying Delay,” Int. J. Robust Nonlinear Control, 21(3), pp. 309–327. [CrossRef]
Xiang, Z. R. , Liu, S. L. , and Chen, Q. W. , 2013, “ Tracking Control for a Class of Switched Non-Linear Systems With Time-Varying Delay,” Trans. Inst. Meas. Control, 35(3), pp. 398–406. [CrossRef]
Lian, J. , and Ge, Y. L. , 2013, “ Robust H∞ Output Tracking Control for Switched Systems Under Asynchronous Switching,” Nonlinear Anal.: Hybrid Syst., 8, pp. 57–68. [CrossRef]
Liberzon, D. , 2003, Switching in Systems and Control, Birkhäuser, Boston, MA. [CrossRef]
Malisoff, M. , and Mazenc, F. , 2009, Constructions of Strict Lyapunov Functions, Springer-Verlag, London. [CrossRef]
Mazenc, F. , Malisoff, M. , and Lin, Z. L. , 2008, “ Further Results on Input-to-State Stability for Nonlinear Systems With Delayed Feedbacks,” Automatica, 44(9), pp. 2415–2421. [CrossRef]
Zhai, J.-Y. , Wang, B. , and Fei, S. M. , 2015, “ Tracking Control for Switched Nonlinear Systems With Multiple Time-Varying Delays,” Nonlinear Anal.: Hybrid Syst., 17, pp. 44–55. [CrossRef]
Wang, Y. E. , Sun, X. M. , and Wu, B. W. , 2015, “ Lyapunov–Krasovskii Functionals for Switched Nonlinear Input Delay Systems Under Asynchronous Switching,” Automatica, 61, pp. 126–133. [CrossRef]
Sun, Z. D. , and Ge, S. S. , 2005, Switched Linear Systems: Control and Design, Springer-Verlag, London. [CrossRef]


Grahic Jump Location
Fig. 1

Response of the switched system with input delay τ¯=0.1 s and w=sin (0.3t) compared with Ref. [25]

Grahic Jump Location
Fig. 2

Schematic of the boost converter

Grahic Jump Location
Fig. 3

The PWM-driven boost converter

Grahic Jump Location
Fig. 4

Response of the switched system with input delay τ¯=0.05 s and x(0)=[00], xr(0)=[22]



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In