Approximate controllability of neutral stochastic evolution differential systems with poisson jump

Controllability of linear impulsive stochastic systems in Hilbert spaces

Neutral stochastic dynamic systems have received broad attention, because the problems are not only great theoretical significance, but also have played an important role in many ways such as engineering control, finance, communication equipment, social science, etc. In this paper, we consider stability of neutral stochastic partial differential dynamic systems with Markovian switching. Some new sufficient conditions proving the stability in mean square of this neutral stochastic dynamic systems are derived by employing the fixed point approach. Some well-known results are improved and generalized.

<p>In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work.</p>

In this paper, under the assumption that the corresponding linear system is approximately controllable, we obtain the approximate controllability of semilinear fractional evolution systems in Hilbert spaces. The approximate controllability results are proved by means of the Hölder inequality, the Banach contraction mapping principle, and the Schauder fixed point theorem. We also discuss the existence of optimal controls for semilinear fractional controlled systems. Finally, an example is also given to illustrate the applications of the main results. MSC:26A33, 49J15, 49K27, 93B05, 93C25.

The classical theory of controllability and observability for deterministic systems is extended to linear stochastic time-varying systems defined on infinite dimensional Hilbert spaces. Two types of stochastic controllability (observability) are studied: approximate and complete controllability (observability). Tests for complete and approximate controllability (observability) are proved, and the relation between the controllability (observability) of linear stochastic systems and the controllability (observability) of the corresponding deterministic systems is studied.

Robust stability of uncertain neutral linear stochastic differential delay system

The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1<q≤2 and are derived by using stochastic analysis theory, fixed point technique, q-order cosine family {<i>C_a</i>(<i>t</i>)}_<i>t</i>≥0, new set of novel sufficient conditions and methods adopted directly from deterministic fractional equations for the second order nonlinear impulsive fractional nonlocal stochastic differential systems with state-dependent delay and Poisson jumps in Hildert space H. Finally an example is added to illustrate the main results.

The stability of stochastic dynamic systems have widespread application prospects and greater theoretical significance. Its theory are mainly applied to engineering control, communication equipment, military technology, biology, finance, etc. In this article, we consider the stability of a Class of nonlinear impulsive neutral stochastic differential dynamic systems. A new set of conditions proving the mean square stability of this nonlinear impulsive neutral stochastic dynamic systems are derived by means of the Banach fixed point theorem. Some well-known results are improved and generalized.

Exact null controllability of semilinear integrodifferential systems in Hilbert spaces

This article discusses pth () moment polynomial integral input-to-state stability (iISS) and -weighted integral input-to-state stability (-weighted iISS) of the switched neutral pantograph stochastic hybrid systems with Lévy noise (SNPSHSs-LN) provided that all dynamical subsystems are input-to-state stability (ISS). Under the linear growth hypothesis, the criteria of ISS-type characterisation are deduced by using random analysis techniques, Lyapunov stability theory and some useful inequality techniques on the basis of the dynamic conditions of the system itself, which is an improvement on existing results about neutral systems. Finally, the theoretical results are demonstrated with a numerical example.

Semilinear stochastic dynamic systems in a separable Hilbert space often model some evolution phenomena arising in physics and engineering. In this paper, we study the existence and uniqueness of mild solutions to neutral semilinear stochastic functional dynamic systems under local non-Lipschitz conditions on the coefficients by means of the stopping time technique. We especially generalize and improve the results that appeared in Govinadan (2005), Bao and Hou (2010), and Jiang and Shen (2011).

Sufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.

In this paper, we present a study on mean square approximate controllability and finite-dimensional mean exact controllability for the system governed by linear/semilinear infinite-dimensional stochastic evolution equations. We introduce a stochastic resolvent-like operator and, using this operator, we formulate a criterion for mean square finite-approximate controllability of linear stochastic evolution systems. A control is also found that provides finite-dimensional mean exact controllability in addition to the requirement of approximate mean square controllability. Under the assumption of approximate mean square controllability of the associated linear stochastic system, we obtain sufficient conditions for the mean square finite-approximate controllability of a semilinear stochastic systems with non-Lipschitz drift and diffusion coefficients using the Picard-type iterations. An application to stochastic heat conduction equations is considered.

This paper studies the design problem of robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filter for neutral stochastic uncertain delay systems. Aiming at neutral stochastic delay systems with polytopic uncertainty, we deduce sufficient conditions of the existence of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filter, and express them into a form of the linear matrix inequality (LMI), then utilize schur complement lemma transformed them into LMIs which can be solved. At last we utilize standard digital software to get filter parameters. The feasibility of the methods of design filter for neutral stochastic uncertain delay systems is demonstrated by numerical examples.

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 &amp; Sons, Ltd.