Investigation of interval stability of linear systems of neutraltype of Lyapunov function method

[摘要] Systems of differential equations with deviating argument of neutral type [1, 3, 8]are used. The mathematical model takes into account not only the previousmoments of time, but also the speed of their change. These equations moreadequately describe the dynamics of processes, but their investigation facessignificant difficulties. The qualitative behavior of solutions of neutral typesystems includes the features both, differential and difference equations [2, 9].Stability investigations require the smallest size of the delay's speed value [7].Recently, so-called interval, or robust stability theory has received intensivedevelopment. It is based on two theorems of V.L. Kharitonov [4, 5] for scalar:equations. However, difficulties have appeared to obtain similar results forsystems in vector-matrix form. It is even more complicated to derive conditionsof interval stability for systems of differential-difference equations, though thereare results for scalar equation in [6, 10].

[学科分类] 应用数学