Open AccessPartial boundedness analysis: a state‐space transformation method for reshaping the estimated domain of stability
Author(s) -
Liu Xiuchong,
Wang Zhanshan,
Chu Enhui,
Zhang Huaguang
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.0675
Subject(s) - mathematics , bounded function , upper and lower bounds , transformation (genetics) , domain (mathematical analysis) , stability (learning theory) , control theory (sociology) , quadratic equation , state (computer science) , state space , lyapunov function , mathematical analysis , computer science , nonlinear system , algorithm , geometry , control (management) , biochemistry , chemistry , statistics , physics , quantum mechanics , machine learning , artificial intelligence , gene
This study focuses on the problem of the state upper bound estimation for linear systems subject to amplitude‐bounded disturbances. A state‐space transformation method is proposed to reshape the estimated domain of stability, which is used to analyse the upper bound of a part of system states. By analysing the estimated domains of stability corresponding to different quadratic Lyapunov functions (QLFs), a universal expression for the upper bounds of a part of system states is obtained. By minimising the universal expression, an appropriate QLF is designed to gain the less conservative estimation on the upper bound of a part of system states. The proposed method provides a novel way of constructing and selecting the appropriate QLF to obtain the less conservative results on the upper bound of a part of system states. The effectiveness of the method is illustrated by two examples.