TY - JOUR
T1 - Quadratic stabilisation of switched affine systems
AU - Xiao, Minqing
AU - Zhai, Guisheng
AU - Huang, Chi
N1 - Funding Information:
This research has been supported in part by National Science Foundation of Fujian Province of China under Grant 2017J01567, and the Fundamental Research Funds for the Central Universities under grant no. JBK190502; Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (C) 21560471. The authors would like to thank Prof. Yufang Chang and Prof. Bo Fu with Hubei University of Technology for valuable discussion.
Publisher Copyright:
© 2019, © 2019 Northeastern University, China.
PY - 2020/1/2
Y1 - 2020/1/2
N2 - We deal with quadratic stabilisation for switched systems which are composed of a finite set of affine subsystems, where both subsystem matrices and affine vectors in the vector fields are switched independently, and no single subsystem has desired quadratic stability. We show that if a convex combination of subsystem matrices is Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law and an output-dependent switching law such that the entire switched system is quadratically stable at the origin. If the convex combination of affine vectors is not zero, we discuss the quadratic stabilisation to a convergence set defined by the convex combination of subsystem matrices and that of affine vectors. We extend the discussion to switched uncertain affine systems with norm bounded uncertainties, and establish a quadratically stabilising state-dependent switching law based on an (Formula presented.) norm condition for a combination of subsystems. Several numerical examples show effectiveness of the results.
AB - We deal with quadratic stabilisation for switched systems which are composed of a finite set of affine subsystems, where both subsystem matrices and affine vectors in the vector fields are switched independently, and no single subsystem has desired quadratic stability. We show that if a convex combination of subsystem matrices is Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law and an output-dependent switching law such that the entire switched system is quadratically stable at the origin. If the convex combination of affine vectors is not zero, we discuss the quadratic stabilisation to a convergence set defined by the convex combination of subsystem matrices and that of affine vectors. We extend the discussion to switched uncertain affine systems with norm bounded uncertainties, and establish a quadratically stabilising state-dependent switching law based on an (Formula presented.) norm condition for a combination of subsystems. Several numerical examples show effectiveness of the results.
KW - LMIs
KW - Switched affine systems (SAS)
KW - convergence set
KW - convex combination
KW - norm bounded uncertainties
KW - output-dependent switching
KW - quadratic stabilisation
KW - state-dependent switching
KW - switched uncertain affine systems (SUAS)
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U2 - 10.1080/23307706.2019.1691065
DO - 10.1080/23307706.2019.1691065
M3 - Article
AN - SCOPUS:85075021170
SN - 2330-7706
VL - 7
SP - 1
EP - 23
JO - Journal of Control and Decision
JF - Journal of Control and Decision
IS - 1
ER -