Robust stability results for nonlinear Markovian jump systems with mode‐dependent time‐varying delays and randomly occurring uncertainties

Abstract

This article is concerned with the robust stability analysis for Markovian jump systems with mode-dependent timevarying delays and randomly occurring uncertainties. Sufficient delay-dependent stability results are derived with the help of stability theory and linear matrix inequality technique using direct delay-decomposition approach. Here, the delay interval is decomposed into two subintervals using the tuning parameter g such that 0 < g < 1, and the sufficient stability conditions are derived for each subintervals. Further, the parameter uncertainties are assumed to be occurring in a random manner. Numerical examples are given to validate the derived theoretical results. V C 2015 Wiley Periodicals, Inc. Complexity 000: 00-00, 2015

Mixed filter design for nonlinear singular Markovian jump systems with time-varying delays based on a dissipativity performance index

“…Delay-dependent conditions are established for each interval, which ensure SMJS (5) to be stochastically admissible and strictly ( Q , S , R ) - γ -dissipative. From Krishnasamy and Balasubramaniam (2016), we can find that by tuning parameter λ , the delay-decomposition approach can not only lead to less conservatism of the result but also reduce the computation complexity caused by the increase of “m”. On the other hand, compared to the work in Krishnasamy and Balasubramaniam (2016), a more general mode-dependent stochastic LKF is constructed in equation (17) and the reciprocally convex inequality is used in equations (19) and (22), which can improve the result, respectively, as demonstrated in Zhang et al (2013) and Park et al (2011).…”

“…Markovian jump systems (MJSs) are special kinds of stochastic systems and hybrid systems, which have been extensively applied to describe many practical systems whose structures and parameters change abruptly. In the past years, much attention has been paid to various kinds of MJSs (Balasubramaniam et al, 2012; Cui et al, 2016; Jiao et al, 2016; Krishnasamy and Balasubramaniam, 2016; Li et al, 2014; Pasha et al, 2009; Shen et al, 2014a, 2014b, 2015b, 2017a, 2017b; Wei et al, 2016a, 2016b; Wei and Zheng, 2014; Wu et al, 2011, 2014; Xu et al, 2007; Yin et al, 2016; Zhu et al, 2016; Zhuang et al, 2016b, 2016a).…”

“…Wu et al (2010b) investigated the problem of mode-independent filter design, both mode-dependent filters and mode-independent filters were designed in Zhang et al (2013) and Liu et al (2017), and in Shen et al (2016), a general filter that contains mode-dependent and mode-independent filters in a unified framework was designed for discrete-time SMJSs with time-varying delays. In addition, in practice, the impact of a nonlinear perturbation on a control system cannot be ignored (see Balasubramaniam et al (2012), Krishnasamy and Balasubramaniam (2016), Long et al (2014) and Wang et al (2015) for details).…”

Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump

“…Neutral systems as a special type of time-delay systems are often encountered because these systems have a wider application value than the general time-delay systems in many dynamical systems such as bioengineering systems, dynamic systems of offshore platform, and dynamic economic models. Hence, there are so many investigations about timedelay systems [1][2][3][4][5][6][7]. As we all know, the systems inevitably receive the impact of sudden changes in the environment, abrupt failure of components, unexpected changes in system parameters, and so on.…”

H∞ stochastic synchronization for master–slave semi‐Markovian switching system via sliding mode control

“…In fact, many practical dynamical systems may suffer from frequent unpredictable structural changes, such as random failures, repairs of sudden environment disturbances and abrupt variation of the operating point. For some representative literatures on this general topic, please refer to and the references therein for more details. However, Markovian switching systems have many limitations in many practical applications, as the jump time of a Markovian process obeys exponential distribution, and the results obtained for Markovian switching systems are intrinsically conservative due to constant transition rates.…”