New robustness bounds for neutral type delay systems via functionals with prescribed derivative

Abstract

The paper is devoted to the robust stability analysis of linear neutral type time delay systems with a constant delay and norm-bounded uncertainties. The method is based on the Lyapunov–Krasovskii functional with a derivative prescribed as a negative definite quadratic form of the “current” system state, which is considered to be not suitable for the robustness analysis due to the fact that it does not admit a quadratic lower bound. Unlike existing results, our approach does not require the derivative of the functional along the solutions of the perturbed system to be negative definite. Instead, we need just an essential part of the integral of the derivative to be negative. The resulting stability condition is presented in the form of a simple inequality depending on the so-called Lyapunov matrix, under an assumption that the difference operator of the perturbed system is stable. The result is applicable to all exponentially stable systems.