Exponential H_∞ filtering for switched stochastic genetic regulatory networks with random sensor delays

Abstract

The exponential H∞ filtering problem is investigated in this paper for a class of switching‐type stochastic genetic regulatory networks (GRNs) with random sensor delays. The objective is to estimate the true concentrations of the mRNA and protein in the presence of random sensor delays. By using the average dwell time approach, sufficient conditions are derived to ensure the filtering error dynamics are mean‐square exponentially stable with a prescribed H∞ disturbance attenuation level. The filter gains are given in terms of the solution to a set of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed design method.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust stability and $$H_{\infty}$$ H ∞ filter design for neutral stochastic neural networks with parameter uncertainties and time-varying delay

“…As pointed out in [13], the signal zðtÞ of the filter depends on C f , which is to be determined. However, there doesn't exist C f to estimate signal z m ðtÞ and z p ðtÞ in [6,24,26,36,41,43,50]. Although (9) is chosen, there is no filter parameter C f exists in [46].…”

“…The filter parameters A f , B f , C f , D f in [6,24,26,36,41,43,50] are chosen to estimate x m ðtÞ, x p ðtÞ, which are cannot be used to estimate the signal z m ðtÞ, z p ðtÞ. The filter discussed in this paper of the form (9) and (10) is the same as that in [13,47,52].…”

“…Although (9) is chosen, there is no filter parameter C f exists in [46]. In this sense, the filter structure in this paper may be more general that those in [1,6,14,19,24,26,36,41,43,46,50]. Define nðtÞ ¼ ½x T ðtÞx T ðtÞ T ; eðtÞ ¼ zðtÞ ÀẑðtÞ, then the filtering error systems can be written as follows:…”

“…The neural networks studied in [1,6,13,14,24,26,36,41,43,46,50,52] don't include any analysis of neutral phenomena. Although the neutral phenomenon has been investigated in [19], the results in [19] are obtained in deterministic setting rather than stochastic setting.…”

Robust Stabilization and Tracking Control for a Class of Switched Nonlinear Systems

“…A common Lyapunov function for all subsystems was proved to be a necessary and sufficient condition for a switched system to be asymptotically stable or exponentially stable under arbitrary switchings . However, most switched systems in practice, which do not possess a common Lyapunov function, still may be asymptotically or exponentially stable under some properly designed switching laws . It has been widely approved that the MLFs approach presented in is a powerful and effective tool for choosing such switching laws.…”