Asymptotic stability of differential systems with impulsive effects suffered by logic choice

In this paper, we investigate the asymptotic stability of differential systems with impulsive effects suffered by logic choice. First, we give the expression of system with logic selected impulsive effects, which is a hybrid system. Second, by using semi-tensor product, a criterion of asymptotic stability for the system is provided. Third, we study the linearly coupled system with impulsive effects under logic choice and give a sufficient condition for asymptotic stability. Finally, a numerical simulation is given to illustrate the effectiveness of our results.

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

[2]  Jinde Cao,et al.  Anti-periodic solution for delayed cellular neural networks with impulsive effects , 2011 .

[3]  Jitao Sun,et al.  Approximate controllability of stochastic impulsive functional systems with infinite delay , 2012, Autom..

[4]  Yu Zhang,et al.  Stability analysis for impulsive coupled systems on networks , 2013, Neurocomputing.

[5]  Daizhan Cheng,et al.  A Linear Representation of Dynamics of Boolean Networks , 2010, IEEE Transactions on Automatic Control.

[6]  Daizhan Cheng,et al.  Analysis and Control of Boolean Networks , 2011 .

[7]  Feiqi Deng,et al.  Stochastic stabilization of hybrid differential equations , 2012, Autom..

[8]  Piotr Kowalczyk,et al.  Micro-chaotic dynamics due to digital sampling in hybrid systems of Filippov type , 2010 .

[9]  D. Cheng,et al.  Analysis and control of Boolean networks: A semi-tensor product approach , 2010, 2009 7th Asian Control Conference.

[10]  Jitao Sun,et al.  Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects , 2010, J. Frankl. Inst..

[11]  Jinde Cao,et al.  Projective synchronization of a class of delayed chaotic systems via impulsive control , 2009 .

[12]  John M. Davis,et al.  A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems , 2009, 0901.3841.

[13]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[14]  Xinzhi Liu,et al.  The method of Lyapunov functionals and exponential stability of impulsive systems with time delay , 2007 .

[15]  Jinde Cao,et al.  Synchronization of delayed complex dynamical networks with impulsive and stochastic effects , 2011 .

[16]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[17]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[18]  Jin Zhou,et al.  Pinning Complex Delayed Dynamical Networks by a Single Impulsive Controller , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Jinde Cao,et al.  Impulsive synchronization of coupled dynamical networks with nonidentical Duffing oscillators and coupling delays. , 2012, Chaos.

[20]  Honglei Xu,et al.  Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems , 2012, J. Glob. Optim..

[21]  Xinzhi Liu,et al.  Input-to-state stability of impulsive and switching hybrid systems with time-delay , 2011, Autom..

[22]  Jitao Sun,et al.  A geometric approach for reachability and observability of linear switched impulsive systems , 2010 .