Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay

This paper deals with the controllability of a class of impulsive neutral stochastic functional differential inclusions with infinite delay in an abstract space. Sufficient conditions for the controllability are derived with the help of the fixed point theorem for discontinuous multi-valued operators due to Dhage. An example is provided to illustrate the obtained theory.     

Controllability of nonlinear neutral evolution integrodifferential systems

Sufficient conditions for controllability of nonlinear neutral evolution integrodifferential systems in a Banach space are established. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An application to partial integrodifferential equation is given.     

Controllability of perturbed nonlinear stochastic integrodifferential systems

The purpose of this paper is to establish the sufficient conditions concerning the complete controllability of stochastic integrodifferential systems in finite dimensional spaces by using the Banach fixed point theorem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay

In this paper we establish sufficient conditions for the approximate controllability of impulsive neutral functional evolution integrodifferential systems in Hilbert spaces. Also we study the exact controllability of the same system. The conditions are obtained by using Schauder’s fixed point theorem when the operator is compact and the Banach fixed point theorem when the operator is not compact. The results are obtained by using the evolution operators.     

Complete controllability of nonlinear stochastic impulsive functional systems

This paper is concerned with the controllability of a kind of nonlinear stochastic impulsive functional systems. Sufficient conditions for the complete controllability of the nonlinear stochastic impulsive functional systems are obtained by using Schauder fixed-point theorem. A numerical example is given to illustrate the effectiveness of the theoretical results.     

Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces

In this paper sufficient conditions for the controllability of impulsive neutral integrodifferential systems with infinite delay are established. The results are obtained by using the Schauder fixed point theorem.     

Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces

In this work the controllability of fractional impulsive neutral functional integrodifferential systems in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional calculus, a semigroup of operators and Krasnoselskii’s fixed point theorem.     

Controllability of impulsive hybrid integro-differential systems

In this paper we study the sufficient conditions for the complete controllability of hybrid integro-differential control systems.     

Stability properties of nonlinear stochastic impulsive systems with time delay

This article establishes mean square stability and stabilization for stochastic delay systems with impulses. Using Razumikhin methodology, two approaches, classical Lyapunov-based method and comparison principle, are proposed to develop sufficient conditions that guarantee the stability and stabilization properties. It is shown that if the continuous system is stable and the impulses are destabilizing, the impulses should not be applied frequently. On the other hand, if the continuous system is unstable, but the impulses are stabilizing, the impulses should occur frequently to compensate the continuous state growth. Numerical examples are also presented to clarify the proposed theoretical results.     

Controllability of nonlinear systems

Some sufficient conditions are presented for the controllability of general nonlinear systems. First, the controllability problem is transformed into the problem of existence of fixed points for some operator; using Schauder's theorem, it is derived that a sufficient condition for controllability is the existence of a subsetS inC _n+m (T) which is invariant for a derived operator. Secondly, with the aid of the notion of comparison principle, the existence of the subsetS is guaranteed by the existence of solutions for some nonlinear integral inequality or equality equations. For example, one solution for such nonlinear integral equations is obtained under the assumption of the uniform boundedness for a nonlinear term of the differential equation.     

Controllability of nonlinear systems

In this paper we obtain global controllability of a semilinear system involving monotone nonlinearities of both Lipschitzian and non-Lipschitzian types.     

Controllability of non-densely defined impulsive neutral functional differential systems with infinite delay in Banach spaces

In this paper, we investigate the controllability for a class of abstract impulsive neutral functional differential systems with infinite delay where the linear part is non-densely defined and satisfies the Hille–Yosida condition. The approach used is the Schauder fixed point theorem combined with the operator semigroups. Particularly, the compactness of the operator semigroups is not needed in this article.     

Controllability in nonlinear systems

In this paper we obtain an explicit expression for the reachable set for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.     

Controllability of fractional impulsive neutral integrodifferential systems with a nonlocal Cauchy condition in Banach spaces

In this work the controllability of fractional impulsive neutral functional integrodifferential systems with a nonlocal Cauchy condition in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional powers of operators and the Banach contraction mapping theorem.     

Controllability of impulsive neutral functional differential inclusions with infinite delay

The paper is concerned with the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in a Banach space. Sufficient conditions for controllability are obtained by using a fixed point theorem for condensing maps due to Martelli. As an application, we also consider an impulsive neutral partial functional differential equation.     

Controllability of nonlinear delay systems

A necessary and sufficient condition for complete controllability of differential systems with delay is proved, which extends analogous results for usual differential systems.     

Controllability of stochastic Volterra integrodifferential systems

In this paper, sufficient conditions for the controllability of stochastic integrodifferential systems in Banach spaces are established. The results are obtained by using a fixed point theorem. An example is provided to illustrate the theory.     

Controllability and observability of impulsive hybrid dynamic systems

Corresponding author, Email: cbsoh{at}auto.eee.ntu.ac.sg This paper considers the controllability and observability ofhybrid dynamic systems with impulsive switching of the otherwisecontinuously evolving state. It derives necessary and sufficientconditions for impulsive hybrid dynamic systems to be controllableand observable.