Controllability of nonlocal boundary conditions for impulsive differential systems of mixed type in banach spaces

It is well-known that controllability is closely linked to pole assignment, structural decomposition, quadratic optimal control and observer design, then the study of controllability plays an important role in the control theory and engineering. In this paper, using the monch fixed point theorem and estimate step by step, controllability of nonlocal boundary conditions for impulsive differential systems of mixed type in Banach spaces is investigated. Under weaker conditions, some sufficient conditions for controllability are obtained. The results improve and extend some known results. An example to illustrate the application of main results is also given.

[1]  Lishan Liu,et al.  Existence theorems of global solutions of initial value problems for nonlinear integrodifferential equations of mixed type in banach spaces and applications , 2004 .

[2]  Min Wang,et al.  Controllability of impulsive differential systems with nonlocal conditions , 2011, Appl. Math. Comput..

[3]  Zhengguo Li,et al.  Analysis and design of impulsive control systems , 2001, IEEE Trans. Autom. Control..

[4]  Jin Liang,et al.  Nonlocal Cauchy problems governed by compact operator families , 2004 .

[5]  Lishan Liu,et al.  Initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces , 2006 .

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

[7]  Rathinasamy Sakthivel,et al.  Approximate controllability of impulsive differential equations with state-dependent delay , 2010, Int. J. Control.

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

[9]  Krishnan Balachandran,et al.  Controllability of second-order integrodifferential evolution systems in Banach spaces , 2005 .

[10]  Hans-Peter Heinz,et al.  On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions , 1983 .

[11]  The solutions of initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces , 2007 .

[12]  Sergiu Aizicovici,et al.  Existence results for a class of abstract nonlocal Cauchy problems , 2000 .

[13]  Zhixin Tai.  Controllability of fractional impulsive neutral integrodifferential systems with a nonlocal Cauchy condition in Banach spaces , 2011, Appl. Math. Lett..

[14]  Shu Wen,et al.  Nonlocal Cauchy Problem for Impulsive Differential Equations in Banach Spaces , 2010 .

[15]  V. Lakshmikantham,et al.  Nonlinear Integral Equations in Abstract Spaces , 1996 .

[16]  Dajun Guo,et al.  A boundary value problem for nth order integro-differential equations in a Banach space , 2003, Appl. Math. Comput..

[17]  Yong-Kui Chang,et al.  Controllability of impulsive functional differential systems with infinite delay in Banach spaces , 2007 .