Improved results on the stability analysis of linear neutral systems with delay decay approach

Abstract

In this paper, the investigation of the asymptotical stability of linear neutral systems with time-varying delay has been presented. In order to achieve the desired results, the integral inequality approach was used to express relationships between terms of Newton-Leibniz formula technique and was constructed an appropriate Lyapunov-Krasovskii functional. By improving a delay decay approach, the stability criteria for the zero solution of system were formulated as linear matrix inequalities (LMIs) which can be easily solved.Two numerical examples have been given to show the applicability of established assumptions and the effectiveness of proposed method by MATLAB-Simulink.

Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method

“…Subsequently, these equations have been frequently used in technical fields of scientific and engineering. Volterra integro-differential equations (VIDEs), which are known as a famous mathematical model in the related literature, and delay differential equations/systems have been seen in many practical fields such as electrical circuit, glass forming process, biology, physics, chemistry, control theory, economics (see, [1][2][3][4][5][6][7][8][9][10][11][12][13]). Besides, many researchers have done studies on the qualitative behaviors of solutions and some numerical solutions of these equations in recent years.…”