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.
