Homogeneous S-Lemma and its application to asymptotic stability of a class of switched nonlinear systems
This paper extends the strict S-Lemma proposed by Yakubovich and uses the improved strict S-Lemma to investigate the asymptotic stability of a class of switched nonlinear systems. First, the strict S-Lemma is extended from quadratic forms to homogeneous polynomials, where the improved S-Lemma is named the strict homogeneous S-Lemma (short for the SHSLemma). Then by utilizing the SHS-Lemma, it is proved that a switched nonlinear polynomial system with two sub-systems admits a Lyapunov function with homogeneous derivative (short for LFHD) if and only if it has a convex combination of the vector fields of its two sub-systems that admits a LFHD. Furthermore, it is shown that the “if part of the former property still holds for switched polynomial systems with three or more sub-systems but the “only if part does not even for switched linear systems.
Strict homogeneous S-Lemma Switched nonlinear systems Lyapunov function with homogeneous derivative Convex combination
ZHANG Kuize ZHANG Lijun
College of Automation, Harbin Engineering University, Harbin 150001, P. R. China School of Marine Technology, Northwestern Polytechnical University, Xi’an 710072, P. R. China
国际会议
The 31st Chinese Control Conference(第三十一届中国控制会议)
合肥
英文
442-447
2012-07-01（万方平台首次上网日期，不代表论文的发表时间）