TY - JOUR
T1 - Stability analysis and failure tolerant control for discrete-time linear systems with controller failure
AU - Xiang, Weiming
AU - Zhai, Guisheng
AU - Xiao, Jian
N1 - Funding Information:
The work of Weiming Xiang and Jian Xiao was supported by the National Natural Science Foundation of China [grant number 51177137], [grant number 61134001]. The work of Guisheng Zhai was partially supported by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (C) 25420451.
Publisher Copyright:
© 2014 Taylor & Francis.
PY - 2015/3/4
Y1 - 2015/3/4
N2 - In this paper, the stability and failure tolerant control are investigated for discrete-time time-invariant linear systems with occasional controller failure due to physical or purposeful reason. By introducing the conceptions of minimal controller reliable time and maximal controller failure time, a novel time-varying piecewise quadratic Lyapunov function (TPQLF) approach is proposed to analyse the stability property of closed-loop system in presence of controller failure. The presented TPQLF method combines both merits of previous Lyapunov function based results such as common Lyapunov function and piecewise Lyapunov function approaches. Furthermore, based on TPQLF, the feasible region described by pairs of minimal controller reliable time and maximal controller failure time can be easily computed by an iterative algorithm. Then, on the basis of the analysis results, time-varying state feedback gains are formulated to construct failure tolerant controller. It is demonstrated that the time-varying structure of controller provides more failure tolerance capacity than time-invariant controller. Several numerical examples are given to illustrate our theoretic findings in this paper.
AB - In this paper, the stability and failure tolerant control are investigated for discrete-time time-invariant linear systems with occasional controller failure due to physical or purposeful reason. By introducing the conceptions of minimal controller reliable time and maximal controller failure time, a novel time-varying piecewise quadratic Lyapunov function (TPQLF) approach is proposed to analyse the stability property of closed-loop system in presence of controller failure. The presented TPQLF method combines both merits of previous Lyapunov function based results such as common Lyapunov function and piecewise Lyapunov function approaches. Furthermore, based on TPQLF, the feasible region described by pairs of minimal controller reliable time and maximal controller failure time can be easily computed by an iterative algorithm. Then, on the basis of the analysis results, time-varying state feedback gains are formulated to construct failure tolerant controller. It is demonstrated that the time-varying structure of controller provides more failure tolerance capacity than time-invariant controller. Several numerical examples are given to illustrate our theoretic findings in this paper.
KW - controller failure
KW - exponential stability
KW - failure tolerant control
KW - time-varying piecewise quadratic Lyapunov function
UR - http://www.scopus.com/inward/record.url?scp=84922023833&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84922023833&partnerID=8YFLogxK
U2 - 10.1080/00207179.2014.966325
DO - 10.1080/00207179.2014.966325
M3 - Article
AN - SCOPUS:84922023833
SN - 0020-7179
VL - 88
SP - 559
EP - 570
JO - International Journal of Control
JF - International Journal of Control
IS - 3
ER -