Set-Valued Mappings and Differential Inclusions

  • Zhengzhi Han
  • Xiushan Cai
  • Jun Huang
Chapter
First Online:
Part of the Springer Tracts in Mechanical Engineering book series (SPTME)

Abstract

This chapter deals with two fundamental concepts for the control systems described by deferential inclusions. They are set-valued mappings and differential inclusions. The first two sections introduce the set-valued mappings and the succeeding four sections involve the differential inclusions.

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References

  1. Aubin J-P, Cellina A (1984) Differential inclusions – set-valued maps and viability theory [M]. Springer, BerlinMATHGoogle Scholar
  2. Cai X, Liu L, Zhang W (2009) Saturated control design for linear differential inclusions subject to disturbance. Nonlinear Dyn 58(3):487–496MathSciNetCrossRefMATHGoogle Scholar
  3. Filippov AF (1988) Differential equations with discontinuous right-hand sides [M]. Kluwer Academic Publishers, DordrechtCrossRefMATHGoogle Scholar
  4. Sontag ED (1989) Smooth stabilization implies coprime factorization [J]. IEEE Trans Autom Control 34(4):435–442MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Shanghai Jiao Tong University Press, Shanghai and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Zhengzhi Han
    • 1
  • Xiushan Cai
    • 2
  • Jun Huang
    • 3
  1. 1.Shanghai Jiao Tong UniversityShanghaiChina
  2. 2.Zhejiang Normal UniversityJinhuaChina
  3. 3.Soochow UniversitySuzhouChina

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