Non Linear Control System Based Modeling of Cardiac Muscle using Describing Function and Lyapnuov Stability.

Abstract

Main focus of this research work is aims towards the nonlinear analysis of human cardiac muscle by describing function technique and finding stability using lyapnuov stability theory. The nature of cardiac muscle can be modeled by mass, spring with a damper where for simplicity spring and damper are considered a linear element. In reality, it has been observed that, the characteristics of spring and damper are not linear rather nonlinear. Not only that, transportation delay (non-zero reaction time) or lag phase of cardiac muscle plays an important role to make the overall model nonlinear. The range of transportation delay for which the system is stable has been calculated here to ensure the presence of dead zone type nonlinearity in cardiac muscle. In this paper a nonlinear characteristics of the model has been analyzed considering dead zone combined with saturation. The describing function technique is used here to represent the nonlinearity. A converging stable limit cycle has been found after the analysis. Finally, lyapnuov stability theorem is applied on our proposed model and it has been that the system is asymptotically stable in the sense of lyapnuov.