中国物理B ›› 2010, Vol. 19 ›› Issue (12): 120512-120512.doi: 10.1088/1674-1056/19/12/120512

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A novel extended Tsypkin criterion for discrete-time descriptor systems with ferromagnetic hysteresis nonlinear physical phenomenon

张庆灵1, 张化光2, 宋铮2   

  1. (1)Institute of Systems Science, Northeastern University, Shenyang 110819, China; (2)School of Information Science and Engineering, Northeastern University, Shenyang 110819, China;Key Laboratory of Integrated Automation of Process Industry (Northeastern University) of National Education Ministry, Shenyang 110819, China
  • 收稿日期:2010-03-07 修回日期:2010-05-10 出版日期:2010-12-15 发布日期:2010-12-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008, 60821063 and 61034005), and National Basic Research Program of China (Grant No. 2009CB32060).

A novel extended Tsypkin criterion for discrete-time descriptor systems with ferromagnetic hysteresis nonlinear physical phenomenon

Zhang Hua-Guang(张化光)a)b)†, Song Zheng(宋铮)a)b), and Zhang Qing-Ling(张庆灵)c)   

  1. a School of Information Science and Engineering, Northeastern University, Shenyang 110819, China; b Key Laboratory of Integrated Automation of Process Industry (Northeastern University) of National Education Ministry, Shenyang 110819, China; c Institute of Systems Science, Northeastern University, Shenyang 110819, China
  • Received:2010-03-07 Revised:2010-05-10 Online:2010-12-15 Published:2010-12-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008, 60821063 and 61034005), and National Basic Research Program of China (Grant No. 2009CB32060).

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摘要： This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input–output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.

Abstract: This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input–output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.

Key words: ferromagnetic hysteresis nonlinearity, discrete-time descriptor systems, extended Tsypkin criterion

中图分类号:  (Magnetization curves, hysteresis, Barkhausen and related effects)

  • 75.60.Ej