Non-fragile observer design
for nonlinear switched systems
with time delay
Zhengrong Xiang and Ronghao Wang
School of Automation, Nanjing University of Science and Technology,
Nanjing, People’s Republic of China
Purpose – The purpose of this paper is to present the non-fragile observer design method for
nonlinear switched systems with time delay.
Design/methodology/approach – Based on dwell time approach and linear matrix inequalities
(LMIs) technology, an exponential stability criterion for the delay switched system with Lipschitz
nonlinearity is presented. By using the key technical lemma, the observer design problem can be
transferred to the problem of solving a set of LMIs. Moreover, non-fragile observer is designed by the
Schur complement lemma, and the result is also transferred to LMIs, which can be easily realized
by MATLAB toolbox.
Findings – Non-fragile observer design is more effective than the common one and is robust to the
observer gain variations.
Originality/value – The proposed non-fragile observer guarantees the estimated state error
dynamics can be exponentially convergent for observer gain perturbations.
Keywords Systems theory, Switching systems, Switching theory, Error analysis
Paper type Research paper
Switched systems have attracted the interest of several scientists in the last 20 years.
Typically, a switched system consists of a number of subsystems and a switching law,
which deﬁnes a speciﬁc subsystem being activated during a certain interval of time.
Study of switched systems mainly focuses on stability and stabilization. A number of
works in this direction have appeared recently (Sun and Ge, 2005; Sun, 2006, 2004; Lin
and Antsaklis, 2005). Cheng et al. (2005) studied the stabilization problem of systems
that switch among a ﬁnite set of controllable linear systems with arbitrary switching
frequency. A series of methods and conditions based on common quadratic Lyapunov
functions (CQLFs) have been given for analyzing the stability of switched systems for
arbitrary switching law. In the study of stability analysis for switched systems,
multiple Lyapunov functions approach has been shown to be an effective tool
(Hespanha et al., 2005; Pettersson, 2005). Hespanha (2004) addressed the uniform
stability of switched linear systems using multiple Lyapunov functions. Most recently,
on the basis of dwell time analysis method, the stability for switched systems have
been further investigated. de Persis et al. (2002, 2003) considered the asymptotic
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This work was supported by the Natural Science Foundation of Jiangsu Province of China under
Grant No. BK2007210 and the Research and Development Foundation from Nanjing University
of Science and Technology under Grant No. AB96248.
Received 28 March 2008
Revised 1 July 2008
Accepted 15 July 2008
International Journal of Intelligent
Computing and Cybernetics
Vol. 2 No. 1, 2009
q Emerald Group Publishing Limited