Stability Of Coupled Control System On Network

Coupled control system on network has a wide range of applications in many areas,such as, artificial intelligence, neural networks, engineering, natural sciences and so on.So more and more scholars and researchers have concerned with the questions aboutcoupled control system on network in recent decades. It is well known that stability hasbeen a focus issue for the scientific community, due to a wide range of practical signifi-cance and application value for stability studies. Thus stability has been a center issuefor many scholars to research all the time. Hence, researching coupled control system’sstability issues on network for theoretical value and practical significance is especiallyimportant.In the first part of this article, we investigate the stability of coupled system withfeedback control on network. Firstly, a model of feedback control coupled system onnetwork is established. Secondly, the definitions of robustly stable and globally expo-nentially stable for feedback control coupled system on network are respectively pre-sented. Then, by using graph theory and Lyapunov method, sufficient conditions of ro-bust stable and globally exponentially stable for feedback control coupled system onnetwork are respectively derived, and demonstration our results. Finally, some suitableexamples are given to illustrate the results.In the second part of this article, we investigate the stability of stochastic coupledsystem with input control on network. Firstly, a model of input control stochastic cou-pled system on network is established. Secondly, three definitions for input control sto-chastic coupled system on network, is that, two kinds of weight stable and almost surelyglobally exponentially stable are respectively presented. Then, also by using graph the-ory and Lyapunov method, sufficient conditions of three kinds of stable for input controlstochastic coupled system on network are respectively derived. Finally, we will proofour main results.