Solution of systems with the time-delay using the operator w

Abstract

Systems with time-delay are a specific group of dynamic systems. There occurs the time lag of the signal, information or material, which results in the deterioration of the properties of a control circuit if we want to control of such system. The presence of time-delay complicates the synthesis of a control circuit and therefore it is necessary to these systems was described by the differential equations. Laplace transform gives a very simple method of solving these linear differential equations with constant coefficients. The theoretical basis for simple but exact solution gives W-transform that a transcendent solution converts to solve algebraic equations. W image is defined similar as is defined by the Z image of the functions.