A state estimation H∞ issue for discrete-time stochastic impulsive genetic regulatory networks in the presence of leakage, multiple delays and Markovian jumping parameters

Stability for discrete-time uncertain systems with infinite Markov jump and time-delay

“…The discrete-time IMJ systems with time-delay and parametric uncertainties have received little attention. As a matter of fact, the approaches in [29,30] and [31] considered stability and H ∞ state estimation for time-delay systems with finite rather than IMJ. Although exponential stability in mean square (ESMS) was addressed in [17] for discrete IMJ systems, it overlooked time-delay and parametric uncertainties.…”

Improved Delay-Dependent Stability Criterion for Genetic Regulatory Networks with Interval Time-Varying Delays via New Lyapunov Functionals

“…Time delays in mathematical systems have received attention from researchers in the stability analysis which provide a poor performance or even instability of the relevant system [9][10][11][12][13][14][15]. In this reason, the stability analysis problems of genetic regulatory network with time delay have been reported in the literature [6,8,[16][17][18][19][20][21][22][23][24][25][26][27][28]. ey proposed new stability condition and reduced the possible conservativeness caused by the time delay.…”

“…An increasing number of research studies about more complex modelled GRNs has been received attention in the following years, e.g., GRNs with distributed delayed [27], GRNs with nonlinear disturbance [17], leakage delay involved GRNS [22], and impulsive perturbation [24]. e stability problems of GRNs, such as stochastic stability [19], robust stability [18], exponential convergence analysis [28], and discrete-time stochastic stability [6,23] have been also reported in the literature.…”

Nonfragile stabilization for uncertain system with interval time‐varying delays via a new double integral inequality

“…Consequently, the need to deeply study the stability of time‐delay systems (TDSs) is of most importance. Therefore, the stability of TDSs was an energetic research field in the last few years and received considerable attention from the scholar society. Nowadays, several efforts have been paid to the issue of TDSs, and a bunch of related literature have been made in this proposed field based on Lyapunov stability theory by way of linear matrix inequality (LMI) technique .…”

“…In particular, desirable controllers should be able to provide safe tuning margins and tolerate some possible amount of uncertainties in their coefficients. Therefore, it is necessary that any controller should be able to tolerate some uncertainty in parameters, and this stimulates many researchers to study the nonfragile control problems . For example, Liu et al derived sufficient conditions for nonfragile H ∞ filtering for delayed Takagi‐Sugeno fuzzy systems with randomly occurring gain variations.…”