Period dependent averaging of a class of pulse modulated systems. Application to the cardiovascular system

Abstract

In approximating nonlinear systems, averaging theory provides very useful tools, which permit one to obtain simpler mathematical models. The current paper addresses the problem of averaging pulse-frequency modulated systems with constant duty ratios, whose trajectories exhibit a moving average dependent on the modulation period. Because for such systems conventional averaging methods lead to period - independent averaged models, the paper proposes a period-weighted averaging approach, which leads to a period - dependent averaged model (simpler than the original one). The proposed averaging method is further used in a case study involving the cardiovascular system (regarded as a pulse-frequency modulated system). Finally, simulation results illustrate the effectiveness of the proposed averaging method.