Complete controllability of impulsive stochastic integro-differential systems

This paper is concerned with the controllability of impulsive stochastic integro-differential systems. Sufficient conditions of complete controllability for impulsive stochastic integro-differential systems are obtained by using Schaefer's fixed point theorem. A numerical example is provided to show the effectiveness of the proposed results.

[1]  Nazim I. Mahmudov,et al.  Controllability of Linear Stochastic Systems in Hilbert Spaces , 2001 .

[2]  Nazim I. Mahmudov,et al.  Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces , 2003, SIAM J. Control. Optim..

[3]  Nazim I. Mahmudov,et al.  Controllability of non-linear stochastic systems , 2003 .

[4]  Alberto Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 2000, IEEE Trans. Autom. Control..

[5]  B. Øksendal Stochastic Differential Equations , 1985 .

[6]  Nazim I. Mahmudov,et al.  Controllability of semilinear stochastic systems in Hilbert spaces , 2003 .

[7]  Nazim I. Mahmudov Controllability of linear stochastic systems , 2001, IEEE Trans. Autom. Control..

[8]  Krishnan Balachandran,et al.  Controllability of semilinear stochastic integrodifferential systems , 2007, Kybernetika.

[9]  Ta-Tsien Li,et al.  Exact Boundary Controllability for Quasi-Linear Hyperbolic Systems , 2002, SIAM J. Control. Optim..

[10]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[11]  Krishnan Balachandran,et al.  Controllability of nonlinear stochastic neutral impulsive systems , 2009 .

[12]  Fengqin Zhang,et al.  Controllability of impulsive functional differential systems in Banach spaces , 2006 .

[13]  Krishnan Balachandran,et al.  Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces , 2009 .

[14]  Rathinasamy Sakthivel,et al.  On controllability of second order nonlinear impulsive differential systems , 2009 .

[15]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[16]  Bin Liu,et al.  Stability of Solutions for Stochastic Impulsive Systems via Comparison Approach , 2008, IEEE Transactions on Automatic Control.

[17]  Rathinasamy Sakthivel,et al.  Controllability of non-linear impulsive stochastic systems , 2009, Int. J. Control.

[18]  Horacio J. Marquez,et al.  Controllability and Observability for a Class of Controlled Switching Impulsive Systems , 2008, IEEE Transactions on Automatic Control.

[19]  Guangming Xie,et al.  Necessary and sufficient conditions for controllability and observability of switched impulsive control systems , 2004, IEEE Transactions on Automatic Control.

[20]  Jitao Sun,et al.  On hybrid control of a class of stochastic non-linear Markovian switching systems , 2008, Autom..

[21]  Nazim I. Mahmudov,et al.  On controllability of nonlinear stochastic systems , 2006 .

[22]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[23]  Xinghuo Yu,et al.  On controllability and observability for a class of impulsive systems , 2002, Syst. Control. Lett..

[24]  A. Shen,et al.  Fixed point theorem , 2002 .

[25]  B. O'neill,et al.  A fixed point theorem , 1957 .

[26]  Ping Zhao,et al.  Practical stability, controllability and optimal control of stochastic Markovian jump systems with time-delays , 2008, Autom..

[27]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[28]  D. Whittaker,et al.  A Course in Functional Analysis , 1991, The Mathematical Gazette.

[29]  Krishnan Balachandran,et al.  Controllability of nonlinear Itô type stochastic integrodifferential systems , 2008, J. Frankl. Inst..