TY - JOUR
T1 - Quadratic stabilizability of switched linear systems with polytopic uncertainties
AU - Zhai, Guisheng
AU - Lin, Hai
AU - Antsaklis, Panos J.
N1 - Funding Information:
The authors would like to thank the editor and the anonymous reviewers for their detailed comments which greatly contributed to this paper. This work has been supported in part by Japanese Society for the Promotion of Science under the Grant-in-Aid for Encouragement of Young Scientists 11750396, and by the National Science Foundation (NSF ECS99-12458 and CCR01-13131).
PY - 2003/5/10
Y1 - 2003/5/10
N2 - In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuous-time switched linear systems, we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback. For discrete-time switched linear systems, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non-negative scalars and a common positive definite matrix. For both continuous-time and discrete-time switched systems, we propose the switching rules by using the obtained common positive definite matrix.
AB - In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuous-time switched linear systems, we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback. For discrete-time switched linear systems, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non-negative scalars and a common positive definite matrix. For both continuous-time and discrete-time switched systems, we propose the switching rules by using the obtained common positive definite matrix.
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U2 - 10.1080/0020717031000114968
DO - 10.1080/0020717031000114968
M3 - Article
AN - SCOPUS:0142137660
SN - 0020-7179
VL - 76
SP - 747
EP - 753
JO - International Journal of Control
JF - International Journal of Control
IS - 7
ER -