This paper is concerned with the filtering problem for a class of discrete-time uncertain stochastic nonlinear time-delay systems with both the probabilistic missing measurements and external stochastic disturbances. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. Such a probabilistic distribution could be any commonly used discrete distribution over the interval [0 1]. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing, stochastic disturbances, norm-bounded uncertainties as well as stochastic nonlinearities, the error dynamics of the filtering process is exponentially mean-square stable. By using the linear matrix inequality (LMI) method, sufficient conditions are established that ensure the exponential mean-square stability of the filtering error, and then the filter parameters are characterized by the solution to a set of LMIs. Illustrative examples are exploited to show the effectiveness of the proposed design procedures.

This paper is concerned with the security control problem with quadratic cost criterion for a class of discretetime stochastic nonlinear systems subject to deception attacks. A definition of security in probability is adopted to account for the transient dynamics of controlled systems. The purpose of the problem under consideration is to design a dynamic output feedback controller such that the prescribed security in probability is guaranteed while obtaining an upper bound of the quadratic cost criterion. First of all, some sufficient conditions with the form of matrix inequalities are established in the framework of the input-to-state stability in probability (ISSiP). Then, an easy-solution version on above inequalities is proposed by carrying out the well-known matrix inverse lemma to obtain both the controller gain and the upper bound. Furthermore, the main results are shown to be extendable to the case of discretetime stochastic linear systems. Finally, two simulation examples are utilized to illustrate the usefulness of the proposed controller design scheme.

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Exponential stability analysis for discrete-time switched linear systems with time-delay," Int. J. Innov. Comput., Inform. Control, vol. 3, no. 6, pp. 1557-1564 [7] L. Zhang, P. Shi, and E. Boukas, " H output-feedback control for switched linear discrete-time systems with time-varying delays," Int. J. Control, vol. 80, no. 8, pp. 1354Control, vol. 80, no. 8, pp. -1365Control, vol. 80, no. 8, pp. , 2007 [8] W. P. Dayawansa and C. F. Martin, "A converse Lyapunov theorem for a class of dynamical systems which undergo switching," IEEE Trans. Automat. Control, vol. 44, no. 4, pp. 751-760, Apr. 1999 Control, vol. 43, no. 4, pp. 555-559, Apr. 1998. [11] J. Geromel and P. Colaneri, "Stability and stabilization of discrete time switched systems," Int. J. Control, vol. 79, no. 7, pp. 719-728, 2006 [28] H. Gao, J. Lam, C. Wang, and S. Xu, " H model reduciton for discrete time-delay systems: Delay-independent and dependent approaches," Int. J. Control, vol. 77, no. 4, pp. 321-335, 2004.[29] S. Xu and J. Lam, " H model reduction for discrete-time singular systems," Syst. Control Lett., vol. 48, pp. 121-133, 2002.[30] C. Gong and B. Su, "Robust L 0 L filtering of convex polyhedral uncertain time-delay fuzzy systems," Int. J. Innov. Comput., Inform. Control, vol. 4, no. 4, pp. 793-802, 2008.[31] L. Zhang, P. Shi, E. Boukas, and C. Wang, "Robust l 0 l filtering for switched linear discrete time-delay systems with polytopic uncertainties," IET Control Theory Appl., vol. Automatica, vol. 37, no. 2, pp. 221-229, 2001. Filtering for Nonlinear Genetic Regulatory Networks With Stochastic DisturbancesZidong Wang, James Lam, Guoliang Wei, Karl Fraser, and Xiaohui LiuAbstract-In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound . By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

In this paper, a delay-dependent approach is developed to deal with the stochastic H ∞ filtering problem for a class of Itô type stochastic time-delay jumping systems subject to both the sensor nonlinearities and the exogenous nonlinear disturbances. The time delays enter into the system states, the sensor nonlinearities and the external nonlinear disturbances. The purpose of the addressed filtering problem is to seek an H ∞ filter such that, in the simultaneous presence of nonlinear disturbances, sensor nonlinearity as well as Markovian jumping parameters, the filtering error dynamics for the stochastic time-delay system is stochastically stable with a guaranteed disturbance rejection attenuation level γ. By using Itô's differential formula and the Lyapunov stability theory, we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist. These conditions are dependent on the length of the time delay. We then characterize the expression of the filter parameters, and use a simulation example to demonstrate the effectiveness of the proposed results. SUBMITTED 2 Consequently, the time delay systems with stochastic perturbations have drawn a lot of attentions from researchers working in related areas, see [1,21,22] and references therein.Markovian jump systems are the hybrid systems with two components in the state [11]. The first one refers to the mode which is described by a continuous-time finite-state Markovian process, and the second one refers to the state which is represented by a system of differential equations. The jump systems have the advantage of modeling the dynamic systems subject to abrupt variation in their structures, such as component failures or repairs, sudden environmental disturbance, changing subsystem interconnections, operating in different point of a nonlinear plant. Recently, filtering and control for Markovian jump systems with or without nonlinear disturbances have drawn some research attentions, see [17,23,24,27,28] for some related results. Note that exogenous nonlinear disturbances may result from the linearization process of an originally highly nonlinear plant or may be an external nonlinear input, and therefore exist in many real-world systems.The filter design problem has long been one of the key problems in the areas of control and signal processing. The purpose of the filtering problem is to estimate the unavailable state variables (or a linear combination of the states) of a given system through noisy measurements. During the past four decades, the filtering problem has been extensively investigated for a variety of complex systems, such as deterministic delay systems [1,8,9], Markovian jumping delay systems [17,20,23] and stochastic delay systems [22,24], to name just a few. When both the Markovian jump parameters and time delays appear in the stochastic systems, the H ∞ filtering problem has been studied in [24], where some useful stochastic stability conditions have been proposed by an LMI technique. In [23], the robust H...