Study On The Stability Of A Kind Of Pulse Switching System With Impulsive Delay

In the study of our actual physical systems and natural science, many mathematical models of practical problems always can be described by impulsive switched functional differential systems, such as network system, the transfer of satellite orbit, communication constraints control. Because of this important practical significance and wide application background, now many scholars at home and abroad devote themselves to this aspect and a lot of interesting results are derived. These results mostly focus on the nonlinear systems with impulsive conditions independent on time delays or the time delays axe finite, however, in practical application, particularly in the design of quick search network capacity and the neutral network optimization calculation, the impulse changes always contain time delays or affected by them indirectly. In addition, impulsive switched functional differential systems with impulsive signal, switching signal and time delay which are more general. Hence, the research on stability theory of impulsive switched functional differential systems has a very important theoretical significance and application value.Consider that the delayed impulse can bing stable and unstable effects to system. In this paper, employing the multiply Lyapunov functionals method and the subsequence method, we mainly studies two impulses impact on system stability. Two main conclusions were given in the following in the view of two kinds of impulses:1) input-to-state stability for a class of impulsive switched nonlinear time-delay systems with delayed impulse effects.The problem of input-to-state stability for a class of impulsive switched nonlinear time-delay systems with delayed impulse effects is investigated. Utilizing the multiple Lyapunov functional method, the input-to-state stability of systems under two kinds of impulses effect were given. Our system is a synthetical one, which contained the switching signals, impulsive signals and delayed impulses. Moreover, a subsequence of the switching and impulsive time sequence is constructed, and the decay of system trajectories has a close relationship with the decay bound, the dwell time bound and the bound of delayed impulses. This implies that our results have a more general result than the other literatures. Finally, the validity and the effectiveness of the results were illustrated by two numerical simulations.2) exponential stability for a class of impulsive switched nonlinear time-delay systems with delayed impulse effects.This section mainly investigate the impact of delayed impulses on the continuous time systems in three aspects, that is, when the continuous time systems is exponentially stable, the continuous time systems is stable and the continuous time systems is not stable, the impulses always make the systems being exponentially stable. Applying the multiple Lyapunov functional technique, conclusions have been generalized to the impulsive switching time delay systems. Two distinct impulses(stable impulses and unstable impulses) were considered in the investigating the stability of systems, and the exponential stability of contained time delay, delayed impulses and switching are derived. The results present that the stability conditions have nothing to do with the initial state. At last, the conclusions were verified by there numerical examples.