TY - JOUR
T1 - Quadratic Performance Analysis of Switched Affine Time-Varying Systems
AU - Li, Wenzhi
AU - Huang, Chi
AU - Zhai, Guisheng
N1 - Funding Information:
This research has been supported in part by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (C) 21560471. It has been jointly aided by the Research Project Supported by the Shanxi Scholarship Council of China under the grant 2015-044, the Fundamental Research Project of Shanxi Province under the grant 2015021085, and the National Science Foundation of China under the grant 61603268.
Publisher Copyright:
© 2018 Wenzhi Li, published by Sciendo.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.
AB - We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.
KW - L2 gain
KW - differential LMIs
KW - observers
KW - quadratic stabilization
KW - switched affine systems
KW - switching law
KW - time-varying systems
KW - tracking
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U2 - 10.2478/amcs-2018-0032
DO - 10.2478/amcs-2018-0032
M3 - Article
AN - SCOPUS:85054853317
SN - 1641-876X
VL - 28
SP - 429
EP - 440
JO - International Journal of Applied Mathematics and Computer Science
JF - International Journal of Applied Mathematics and Computer Science
IS - 3
ER -