Absolute Interval Stability of Indirect Regulating Systems of Neutral Type

On the Interval Stability of Weak-Nonlinear Control Systems with Aftereffect

“…At Shatyrko and Khusainov earlier papers conditions of interval stability of systems (5) using finite-dimensional Lyapunov's functions $\begin{array}{c}T1V\left(x\right)=x^{T}Hx+\beta \underset{\mathrm{normal0}}{\overset{\sigma \left(x\right)}{{\displaystyle false\int }}}f\left(\xi \right)d\xi ,\sigma \left(x\right)=c^{T}x\end{array}$have been obtained [24–27]. …”

“…At the expense of application of the alternative approach of Lyapunov-Krasovskii functional, forms of estimations in sufficient conditions of interval stability are essentially simplified in comparison with obtained analogous one on the basis of finite-dimensional Lyapunov's functions of Lur'e-Postnikov types [24, 25, 34, 35]. …”

“…Distribution of this method on systems with delay and neutral type has been obtained in Shatyrko and Khusainov works [24–27] and numerous works of Chinese scientists (e.g., [5, 28]). Sufficient conditions of absolute interval stability have been constructed.…”

On differential equations with interval coefficients

“…Differential equations with interval coefficients arise also when stability problems are examined. We naturally encounter with the robust (or interval) stability concept when we study real‐life problems in control theory . A system is called robust (interval absolutely stable), if it is absolutely stable for each matrix, the elements of which lie in the specified intervals .…”