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Investigation of interval stability of linear systems of neutral type of Lyapunov function method

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  • Denis Ya. Khusainov

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].

Suggested Citation

  • Denis Ya. Khusainov, 2002. "Investigation of interval stability of linear systems of neutral type of Lyapunov function method," International Journal of Stochastic Analysis, Hindawi, vol. 15, pages 1-11, January.
    • Handle: RePEc:hin:jnijsa:979286
    DOI: 10.1155/S1048953302000072
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