On the uniqueness of the positive solution for a second-order integral boundary value problem with switched nonlinearity

Abstract Applying a fixed point theorem for a concave operator on a cone, this work presents a sufficient condition for the existence and uniqueness of a positive solution for a second-order integral boundary value problem with switched nonlinearity. An example is worked out to illustrate the main results.

[1]  G. Karakostas,et al.  Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. , 2002 .

[2]  Zhilin Yang.  Existence of nontrivial solutions for a nonlinear Sturm–Liouville problem with integral boundary conditions , 2008 .

[3]  Daniel Liberzon,et al.  Lie-Algebraic Stability Criteria for Switched Systems , 2001, SIAM J. Control. Optim..

[4]  Panos J. Antsaklis,et al.  Special issue on hybrid systems: theory and applications a brief introduction to the theory and applications of hybrid systems , 2000, Proc. IEEE.

[5]  O. Stursberg,et al.  Continuous-discrete interactions in chemical processing plants , 2000, Proceedings of the IEEE.

[6]  Hai Lin,et al.  Stabilization and performance analysis for a class of switched systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[7]  Xingqiu Zhang,et al.  On multiple sign-changing solutions for some second-order integral boundary value problems , 2010 .

[8]  Lei Guo,et al.  STABILIZATION OF SWITCHED LINEAR SYSTEMS , 2003, IEEE Trans. Autom. Control..

[9]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[10]  Jean Buisson,et al.  On the Stabilisation of Switching Electrical Power Converters , 2005, HSCC.

[11]  Shihua Li,et al.  Finite-time stability and stabilization of switched linear systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[12]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

[13]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[14]  Fuyi Li,et al.  Sign-changing solutions to second-order integral boundary value problems , 2008 .

[15]  Robert Shorten,et al.  On the Stability of Switched Positive Linear Systems , 2007, IEEE Transactions on Automatic Control.

[16]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[17]  Zhilin Yang,et al.  Positive solutions of a second-order integral boundary value problem , 2006 .

[18]  J. Webb,et al.  Positive solutions of nonlocal boundary value problems involving integral conditions , 2008 .

[19]  Xiaoming Hu,et al.  An Extension of LaSalle's Invariance Principle and Its Application to Multi-Agent Consensus , 2008, IEEE Transactions on Automatic Control.

[20]  Long Wang,et al.  Packet-loss dependent controller design for networked control systems via switched system approach , 2008, 2008 47th IEEE Conference on Decision and Control.