Abstract
Systems of differential equations with deviating argument of neutral type [1, 3, 8] are used. The mathematical model takes into account not only the previous moments of time, but also the speed of their change. These equations more adequately describe the dynamics of processes, but their investigation faces significant difficulties. The qualitative behavior of solutions of neutral type systems 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 intensive development. It is based on two theorems of V.L. Kharitonov [4, 5] for scalar: equations. However, difficulties have appeared to obtain similar results for systems in vector‐matrix form. It is even more complicated to derive conditions of interval stability for systems of differential‐difference equations, though there are results for scalar equation in [6, 10].
Highlights
In this article, sufficient conditions of interval stability are obtained for systems of differential equations with deviating arguments of neutral type: Ð"ÑHere Hß Eß F are matrices with constant coefficients and 7 ! is a constant delay
Sufficient conditions of interval stability are obtained for systems of differential equations with deviating arguments of neutral type: B† Ð>Ñ œ HB† Ð> 7Ñ EBÐ>Ñ FBÐ> 7ÑÞ
Definition 4: The system (2) is called interval stable, if it is asymptotically stable for all matrices ?H, ?E, ?F with elements as given in (3)
Summary
Hß Eß F are matrices with constant coefficients and 7 ! is a constant delay. Along with the system (1) we consider an interval system of following form. Hß Eß F are matrices with constant coefficients and 7 ! Along with the system (1) we consider an interval system of following form. Ð#Ñ where the elements of the matrices ?H œ Ö?.34×, ?E œ Ö?+34×, ?F œ Ö?,34×, 3ß 4 œ "ß 8 take values from some fixed, symmetric intervals. We obtain conditions of interval (robust) stability of the system (2), i.e., asymptotic stability with respect to the matrices ?H, ?E, ?F. Of the system (1) is called asymptotically stable if it is Lyapunov stable and lim ± BÐ>Ñ ± œ !. And in the following, the vector norms are given by:
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