A novel integral inequality and its application to stability analysis of linear system with multiple time delays (Q2060911)

The paper studies the linear system with multiple time delays \[ \begin{cases} \dot{x} (t) = \sum\limits_{i=0}^N A_i x(t-\tau_i), t>0\\ x(t)=\phi(t), t\in [-\tau,0] \end{cases} \] The paper provides a novel inequality in Lemma 3 which is then used to bound the integral terms in the first derivative of the Lyapunov-Krasovskii functional \(V(t)\): \(\dot{V}(t)\leq -\varepsilon \|x(t)\|^2\), which establishes the asymptotic stability of the linear system. Numerical examples are given to illustrate the applicability of the method.