Robust Analysis Of Global Exponential Stability Of Nonlinear Systems With Piecewise Constant Arguments

Owing to the diversity of nonlinear system,the randomness of switching mode and the variability of behavior,it has a wide range of applications in mechanical operation,biological nerve,economic management,circuit communication,automatic control and other fields.In practical engineering,the stability of the system is usually disturbed by a variety of exogenous factors.How much disturbance the original stable neutral system can withstand is a problem worthy of attention and exploration.In this paper,the robustness of global exponential stability of nonlinear dynamical systems with piecewise arguments is studied.By using Gronwall-Bellman inequality and modular inequality techniques,combined with the properties of stochastic differential equations,the upper bound of exogenous disturbances that can keep the system stable is derived by solving multiple implicit transcendental equations.Thus the sufficient criteria for exponential stability of the system are determined.The main work of this paper includes the following aspects:The global exponential stability of recurrent neural networks with piecewise arguments and neutral terms is investigated.Furthermore,the effect of neutral terms on recurrent neural network system is considered.Lipschitz condition and Gronwall inequality are used to establish the quantization criteria of two kinds of exogenous interference factors-piecewise arguments and neutral terms.The robustness of global exponential stability of neural networks equipped with piecewise constant arguments,neutral terms and uncertain connection weights is discussed.When the neural network system is stable after the initial disturbance,the closed region of the strength of the uncertain connection weight matrix that the system can tolerate again is characterized by the established transcendental equation.The robust exponential stability of nonlinear systems with piecewise arguments,neutral terms and stochastic disturbances is explored.Based on the isometric property of stochastic differential equation,the new independent parameters-interdependent variables(IPIV)method is established according to the target multiple implicit transcendental equation to be solved,forming the linkage effect and strong constraint of three kinds of exogenous interference,so as to ensure the efficiency of the quantization mechanism finally derived.In this paper,the generalized stochastic nonlinear system generalizes the neural network model and makes it more flexible and practical.The research on the robustness of several kinds of nonlinear dynamical systems with piecewise arguments can be extended to more different types of nervous systems.The new method can provide an idea for solving a class of implicit multivariable transcendental equation algebraic problems.The quantization criteria and processing method of robustness can be applied to more practical mathematical problems.