The lungs are particularly vulnerable to acute, critical illness. Respiratory failure can result not only from primary lung pathology, such as pneumonia, but also as a secondary consequence of heart failure or inflammatory illness, such as sepsis or trauma. When this occurs, it is essential to support patients with mechanical ventilation while the fundamental disease process is addressed. The goal of mechanical ventilation is to ensure adequate ventilation, which involves a magnitude of gas exchange that leads to the desired blood level of carbon dioxide, and adequate oxygenation that ensures organ function. Achieving these goals is complicated by the fact that mechanical ventilation can actually cause acute lung injury, either by inflating the lungs to excessive volumes or by using excessive pressures to inflate the lungs. Thus, the challenge to mechanical ventilation is to produce the desired blood levels of carbon dioxide and oxygen without causing further acute lung injury. In this research, we develop an analysis and control synthesis framework for a pressure-limited respirator and lung mechanics system using compartment models. Specifically, a general mathematical model is developed for the dynamic behavior of a multicompartment respiratory system. Then, based on this multicompartment model, an optimal respiratory pattern is characterized using classical calculus of variations minimization techniques for inspiratory and expiratory breathing cycles. Furthermore, model predictive controller frameworks are designed to track the given optimal respiratory air flow pattern while satisfying control input amplitude and rate constrains.