Fibromyalgia Syndrome (FMS) and Chronic Fatigue Syndrome (CFS) are complex medical conditions with similar symptoms such as anxiety, fatigue, depression, headaches, muscle aches and joint pain. The etiology of both these syndromes is unknown. The objective of this study is to characterize FMS, both in the presence and in the absence of CFS, by analyzing variations in cortisol secretion patterns, timings, amplitudes, and the number of the underlying pulses as well as infusion and clearance rates. The comparison is performed against matched healthy control subjects. We estimate the hormonal secretory events by deconvolving cortisol data using a two-step coordinate descent approach. The first step implements a sparse recovery approach to infer the amplitudes and the timings of the cortisol secretion events from limited cortisol hormone data. The main advantage of this method is estimating the cortisol secretory events using a system theoretic approach. The second step is to estimate the physiological system parameters (i.e. infusion and clearance rates). This approach has been verified on healthy individuals previously. Our results show that the clearance rate of cortisol by the liver is relatively lower in patients as compared to the matched healthy individuals. This suggests that there is a relatively higher accumulation of serum cortisol in patients when compared to matched healthy subjects.