Robustness Analysis Of Dynamic Network Systems With Deviating Argument

In this paper,we focus on the robustness analysis of several types of dynamic network systems containing deviating argument.The effect of deviating argument on the exponential stability of the dynamic network systems is quantitatively analyzed by using Gronwall Lemma,Lipschitz condition and norm inequality scaling technique in conjunction with stability theory.Through the transcendental equation with adjustment parameters,the supremum of exogenous disturbance that makes the perturbed dynamic network system still exponentially stable is solved,and then the criterion of exponential stability of the perturbed dynamic network system is given.The main work of this paper is summarized as follow.Firstly,the effect of the deviating argument on the controller of a complex dynamic network system is discussed for a given linear controller and a nonlinear controller,respectively.The exponential stability condition of the error system of the complex dynamic network system not only derives the transcendental equation with adjustable parameters,quantifies the supremum of the length of the interval of the deviating argument for the error system of the complex dynamic network system to remain stable,but also provides an idea to investigate the dynamics of the complex dynamic network system with deviating argument.Next,the effects of the deviating argument and the simultaneous action of deviating argument and noise on the stability of Markov dynamic network systems are investigated.Using the transcendental equation with adjustment parameters,a mechanism for quantifying the bounds of two types of exogenous disturbances is established.Not only the robust stability of the Markov dynamic network system with the above two types of disturbances is investigated,but more importantly,it is pointed out that the interval length of the bias function and the upper bound of the noise intensity need to be obtained simultaneously when the deviating argument and noise act simultaneously,the interval length of the deviating argument and the upper bound of the noise intensity need to be obtained simultaneously,instead of being superimposed directly.Finally,the robustness of stochastic dynamic network systems with deviating arguments is analyzed.The exponential stability of stochastic dynamic network system with the presence of deviating arguments only in the drift term is discussed first,followed by the exponential stability of the stochastic dynamic network system with the presence of deviating arguments in both the drift and diffusion terms.The upper bound of the interval length of the deviating arguments at different positions is quantified by the transcendental equation,and the criterion of exponential stability of the stochastic dynamic network system is obtained,and the stability control technique of the stochastic dynamic network system is established.