Delay-dependent stability and stabilization criteria for T-S fuzzy singular systems with interval time-varying delay by improved delay partitioning approach.

Chao Sun,Fuli Wang,Xiqin He

doi:10.1186/s40064-016-1982-2

Chao Sun, Fuli Wang + Show 1 more

Open Access

https://doi.org/10.1186/s40064-016-1982-2

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Abstract

This paper deals with the stability analysis and fuzzy stabilizing controller design for a class of Takagi–Sugeno fuzzy singular systems with interval time-varying delay and linear fractional uncertainties. By decomposing the delay interval into two unequal subintervals and seeking a appropriate ρ, a new Lyapunov–Krasovskii functional is constructed to develop the improved delay-dependent stability criteria, which ensures the considered system to be regular, impulse-free and stable. Furthermore, the desired fuzzy controller gains are also presented by solving a set of strict linear matrix inequalities. Compared with some existing results, the obtained ones give the result with less conservatism. Finally, some examples are given to show the improvement and the effectiveness of the proposed method.

Highlights

During the past few decades, fuzzy technique has been widely used in nonlinear system modelling, especially for systems with incomplete plant information
A number of significant results have been reported to solve the different problems of fuzzy systems, such as stability analysis (Chadli et al 2014; Su et al 2013, 2014b), filter design (Shi et al 2015; Su et al 2014a, 2015), robust control (Mourad et al 2013; Tian et al 2010), etc
It is worth mentioning that, the problem of Hankel-norm output feedback controller design for T–S fuzzy stochastic systems have been investigated in Su et al (2014b)

Summary

Background

During the past few decades, fuzzy technique has been widely used in nonlinear system modelling, especially for systems with incomplete plant information. Some research works on stability analysis (Mourad et al 2013; Zhang et al 2009; Chadli et al 2014; Wang et al 2014) and controller design (Zhu et al 2016; Ma et al 2015; Zhao et al 2015; Han et al 2012) have been extended for T–S fuzzy singular systems with time-varying delay. In Ma et al (2015), a delay-central-point method was presented to develop less conservative delay-dependent conditions for memory dissipative control for fuzzy singular time-varying delay systems under actuator saturation It is well-known that the challenges of deriving a less conservative result are to construct an appropriate LKF that includes more useful state information and to reduce the enlargement in bounding the derivative of LKF as much as possible. Pre-multiplying and post-multiplying the preceding inequality by H T H and its transpose, respectively, since Q1 > 0 and with definitions (18), we can obtain

A Ti22P 22

Conclusion