Delay-Dependent Exponential Stability of Neutral Stochastic Delay Systems

Abstract

This paper studies stability of neutral stochastic delay systems by linear matrix inequality (LMI) approach. Delaydependent criterion for exponential stability is presented and numerical examples are conducted to verify the effectiveness of the proposed method.

Design of sliding-mode observer for a class of uncertain neutral stochastic systems

“…(3) in this paper, which play an important role in many industrial fields. In recent years, increasing efforts have been made to probe the NSS, the main research of which focuses on the stability analysis (e.g., stochastic stability and stability in the mean-square sense, etc) and control of the systems, e.g., Chen, Hu, & Wang (2014) ; ;Chen, Zheng, & Shen (2009) ;Chen, Zheng, & Xue (2010) ;Huang, & Mao (2009) ;Jankovic, Randjelovic, & Jovanovic (2009) ;Song, Xu, Xia, Zou, & Chen (2011);Song, Park, Wu, & Zhang (2013) ;Xu, Chu, Lu, & Zou (2006) ;Xu, Shi, Chu, & Zou (2006) and the references therein. It is noted that, SMC for uncertain NSS without matched uncertainties have been concerned by Chen, & Zhang (2008); Kao, Wang, Xie, Karimi, & Li (2015).…”

“…Based on above conditions, one can verify that the stochastic neutral system (3) with u(t) = 0 has a unique solution according to Huang et al (2009);Mao (2007). In fact, denote the following terms:…”

L2–L∞filter design for a class of neutral stochastic time delay systems

“…In general, these two kinds of time delay are different. That is to say τ = d. However, in [28], [29], [33], [34], the discrete delay is assumed to be equal to the neutral delay. It is too special.…”

“…Based on the slack matrix approach, a less conservatism stability criterion was derived for a class of stochastic time-delay systems with nonlinearities and Markovian jump parameters [27]. Furthermore, by using the free-weighting matrix approach, new delay-dependent stability criteria for neutral stochastic delay systems were proposed in [28], [29]. In addition, delay-partitioning method is another popular technique, an augmented delay partition Lyapunov-Krasovskii functional was constructed to resolve the H ∞ filtering problem of neutral stochastic time-delay systems [30].…”

H ∞ DOF control of stochastic systems with time-varying delay and L ∞ disturbance

“…Both parameter uncertainties and time-varying delays are considered in many stochastic stability problems, moreover, the H ∞ control problem for stochastic systems has been studied in many literatures [10,11]. The stability of stochastic delay interval systems with Markovian switching is considered in [12], robust H ∞ control and H ∞ filtering problem are investigated in [13] for uncertain Markovian jump systems, and [14] presented the delay-dependent exponential stability of neutral stochastic systems. In addition, the disturbance often occurs in stochastic systems, [8,11] consider the H ∞ control problem for uncertain stochastic systems with time-delay and switched stochastic systems respectively.…”