ANALYSIS OF A SYSTEM OF LINEAR DELAY DIFFERENTIAL EQUATIONS USING THE MATRIX LAMBERT FUNCTION

Abstract

Time-delay systems are prevalent across various disciplines, including engineering, biology, economics, and control theory. Their inherent complexity presents challenges in system analysis and control design. In this Project provides a comprehensive overview of recent advancements in solving time-delay systems by classifying functional differential equations and emphasizing the importance of understanding their stability properties. An approach for analytically solving systems of delay differential equations has been developed using the matrix Lambert function. To extend this function for scalar delay differential equations, we introduce a new matrix, e(BT), for situations where the coefficient matrices in a system of delay differential equations do not commute. The solution is expressed as an infinite series of modes using the Lambert function. The advantage of this approach lies in its similarity to the concept of the state transition matrix in linear ordinary differential equations.