Neutral Stochastic Systems Research Articles

Formula omitted] filter design for a class of neutral stochastic time delay systems

This paper is devoted to the problem of L2–L∞ filtering for a class of neutral stochastic systems with different neutral time-delay, discrete delay and distributed delays. By constructing a new Lyapunov–Krasovskii functional, some novel delay-dependent mean-square exponential stability criteria are obtained in terms of linear matrix inequalities. In the derivation process, neither model transformation method nor free-weighting matrix approach is used. Based on the obtained stability criterion, sufficient condition for the existence of the full-order L2–L∞ filter is given by introducing two appropriate slack matrix variables. Desired L2–L∞ filter is designed such that the resulting filtering error system is mean-square exponential stable and a prescribed L2–L∞ disturbance attenuation level is satisfied. Finally, numerical examples are included to illustrate the effectiveness and the benefits of the proposed method.

Stability analysis for neutral stochastic linear system

This study is a further note on stability analysis for uncertain linear neutral stochastic system. Firstly, the stability of linear neutral stochastic system with mix delays is studied. By employing a new Lyapunov–Krasovskii functional and novel method to estimate the integral terms, the less conservative stability criteria are obtained. Compared with previous results, the novel method can sufficiently utilise more negative items information. Then, in virtue of the Schur complement and linear matrix inequality technique, the robust stability of the uncertain neutral stochastic system is derived, which have less conservatism. Finally, two numerical examples show that the authors’ results are effective and less conservative than other reports in the previous literature.

Using waveform relaxation methods to approximate neutral stochastic functional differential equation systems

This paper extends the waveform relaxation (WR) method to neutral stochastic functional differential equations. The linear convergence theory of the continuous time WR method is established in the mean square sense when the coefficients of stochastic differential equation systems satisfy the Lipschitz condition and the contractive mapping. The discrete time WR method based on the Euler scheme, which is used in an actual implementation, was also studied. It turns out that the sequence produced by this method converges linearly to the Euler approximate solution which is convergent. In addition, we prove that the preceding methods are convergent superlinearly if the neutral term does not been split. Finally, the theory is applied to a one-dimensional model problem and checked against results obtained by numerical experiments.

H∞ sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters

This paper is devoted to the investigation of H ∞ sliding mode control (SMC) for uncertain neutral stochastic systems with Markovian jumping parameters and time-varying delays. A sliding surface functional is firstly constructed. Then, the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite-time interval. The sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the efficiency of the proposed method.

New delay-dependent stability of Markovian jump neutral stochastic systems with general unknown transition rates

This paper investigates the delay-dependent stability problem for neutral Markovian jump systems with generally unknown transition rates (GUTRs). In this neutral GUTR model, each transition rate is completely unknown or only its estimate value is known. Based on the study of expectations of the stochastic cross-terms containing the integral, a new stability criterion is derived in terms of linear matrix inequalities. In the mathematical derivation process, bounding stochastic cross-terms, model transformation and free-weighting matrix are not employed for less conservatism. Finally, an example is provided to demonstrate the effectiveness of the proposed results.

Maximum principle for optimal control of neutral stochastic functional differential systems

This paper is concerned with optimal control of neutral stochastic functional differential equations (NSFDEs). The Pontryagin maximum principle is proved for optimal control, where the adjoint equation is a linear neutral backward stochastic functional equation of Volterra type (VNBSFE). The existence and uniqueness of the solution are proved for the general nonlinear VNBSFEs. Under the convexity assumption of the Hamiltonian function, a sufficient condition for the optimality is addressed as well.

Robust delay-range-dependent non-fragile H∞ filtering for uncertain neutral stochastic systems with Markovian switching and mode-dependent time delays

This paper deals with the problem of robust non-fragile H∞ filter design of uncertain neutral stochastic system with Markovian jumping parameters and mode-dependent time delays. The parameter uncertainties are assumed to be norm-bounded. The time delays depend on system modes and vary in an interval. Attention is focused on the design of a non-fragile filter that guarantees the exponential mean-square stability and a prescribed H∞ performance level of the filtering error systems. A delay-range-dependent stability condition in terms of linear matrix inequality(LMI) is derived for the solvability of this problem. Numerical examples compared with the existing results are provided to demonstrate the less complicated and less conservative of the proposed method.

Existence and stability solutions of second-order partial neutral stochastic nonlinear differential systems with infinite delay

In this paper we consider a class of second-order neutral stochastic differential equations with infinite delay. First we establish a new set of sufficient conditions for the existence and uniqueness results for the system of equations which are discussed under non-Lipschitz with Lipschitz condition by the means of the successive approximation and theory of cosine families. Moreover, we give the continuous dependence of solutions on the initial data by the way of corollary of the Bihari's inequality. Finally, an example is provided to illustrate our results.

RobustH∞Filtering for Uncertain Neutral Stochastic Systems with Markovian Jumping Parameters and Time Delay

This paper deals with the robustH∞filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribedH∞performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.

Delay-dependent robust stability of uncertain neutral-type It[formula omitted] stochastic systems with Markovian jumping parameters

This paper investigates the problem of mean-square exponential stability for uncertain neutral stochastic systems with time-delays and Markovian jumping parameters. Based on the new results on expectations of stochastic cross terms containing the Itoˆ integral by Song et al. (2013), a new Lyapunov–Krasovskii function is established, and then an improved mean-square exponential stability criterion is derived. The derived results extend the conclusions recently presented in Song et al. (2013). In fact, the system discussed in Song et al. (2013) is a special case of ours. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.

Exponential stability criteria for a neutral type stochastic single neuron system with time-varying delays

In this paper, the issue of global exponential stability for a neutral type single neuron system with stochastic effects is investigated. Based on the linear matrix inequality (LMI) approach together with a novel Lyapunov–Krasovskii functional and stochastic analysis theory, sufficient conditions are derived to ensure that the considered system with time-varying delays is globally exponentially stable. Numerical examples are provided to demonstrate the efficiency and less conservatism of the derived theoretical results.

Delay‐dependent exponential stability for neutral stochastic system with multiple time‐varying delays

In this study, by constructing an appropriate Lyapunov–Krasovskii functional, one delay-dependent exponential stability criterion of neutral stochastic system with multiple time-varying delays is obtained in terms of linear matrix inequalities. The significant contributions of this study are that the fewer matrix variables in obtained results are involved and some less computational burdens are imposed. In particular, the obtained results can greatly reduce the conservatism when the multiple time-invariant delays case is considered. Finally, three illustrative numerical examples are given to show the effectiveness of our proposed results.

New result on exponential stability for neutral stochastic linear system with time-varying delay

This paper mainly considers the problem for the exponential stability of neutral stochastic linear system with time-varying delay. In the light of a coupled delay-integral inequality and using the stochastic analytic technique, the exponential stability criteria for such systems are given in term of the algebraic inequalities, regardless of whether the time-varying delay is differentiable or not. An illustrative numerical example is given to show the effectiveness of the obtained result.

Delay-dependent robust [formula omitted] filter design for uncertain neutral stochastic systems with mixed delays

This paper is concerned with the problem of the robust L2–L∞ filter design for uncertain neutral stochastic systems with mixed delays. By constructing a modified Lyapunov–Krasovskii functional, some novel delay-dependent exponential stability criteria for uncertain neutral stochastic systems with mixed delays are established in terms of linear matrix inequality. And the obtained stability criteria pave the way for designing the robust L2–L∞ filter to guarantee the robustly exponential stability for the filtering error systems with a prescribed L2–L∞ performance level for all admissible uncertainties. Finally, three illustrative numerical examples are given to show the effectiveness of the obtained results.

Controllability of fractional neutral stochastic functional differential systems

In this paper, we study a class of fractional neutral stochastic functional differential systems. We obtain the controllability of the stochastic functional differential systems by the Sadovskii’s fixed point theorem under some suitable assumptions. An example is given to illustrate the theory.

New results on stability analysis for neutral stochastic linear system

In this study, the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic linear system with mixed time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii functional and utilising a convex polyhedron method, some new delay-dependent exponential stability criteria for such system are established in forms of linear matrix inequalities, which have less conservatism. Finally, three illustrative numerical examples are given to show the effectiveness of the obtained results.

APPROXIMATE CONTROLLABILITY OF FRACTIONAL ORDER NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLOCAL CONDITIONS AND INFINITE DELAY

This paper deals with the approximate controllability of fractional order neutral stochastic integro-differential system with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. The control function for this system is suitably constructed by using the infinite dimensional controllability operator. With this control function, the sufficient conditions for approximate controllability of the proposed probelm in Hilbert space is established. Further, the results are obtained by using fractional calculus, stochastic analysis techniques, Sadovskii fixed point theorem and similar to the classical linear growth condition and the Lipschitz condition. Finally an example is provided to illustrate the application of the obtained results.

An analysis of the exponential stability of linear stochastic neutral delay systems

SummaryThis paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches hmax, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.

A novel result on stability analysis for uncertain neutral stochastic time-varying delay systems

This paper is concerned with the mean-square exponential stability analysis for uncertain neutral linear stochastic time-varying delay systems. By Lyapunov–Krasovskii theory and linear matrix inequality method, under the generalized Finsler lemma (GFL) framework, delay-dependent mean-square exponential stability criteria are established without involving model transformation, cross-terms bounding technique or additional free-weighting matrix. Moreover, GFL is also employed to obtain stability criteria for a class of uncertain linear stochastic neutral systems with different discrete and neutral delays. Numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing results.

Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces

Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approximate controllability of control systems governed by a class of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established under the natural assumption that the corresponding linear system is approximately controllable. The results are obtained by using semigroup theory, stochastic analysis techniques, fixed point approach and abstract phase space axioms. An example is provided to illustrate the application of the obtained results.