State-space analysis of fractional-order respiratory system models. (March 2020) - Saatci, Esra; Saatci, Ertugrul
Highlights: State-space representations of the fractional-order respiratory system models provide timevarying nature of the system incorporated by the parameters. Control system analysis methods were applied to test the dynamics of the continuous time system evaluated by the already estimated parameter values in the literature. Controllability and observability tests revealed that for some models cannot provide a solution for a given input and output signals. Sufficient asymptotic stability bounds were driven by using stability theory of the discrete timedelay system. It is proved mathematically that lower fractional orders have some consequences in the stability of FOMs. Abstract: Fractional Order Models (FOM) of the respiratory system have been used in the model-based analysis of the respiratory system. Although there are studies exploring the physiological correctness and fitting accuracy of the models, they are not analyzed in terms of interactions between parameters, time-varying dynamics and measurable signals. In this study we purpose to use state-space analysis to yield the time-varying nature of the system incorporated by the parameters, states and output. We tested the models for controllability, observability and stability characteristics while using the parameters found in the literature. Sufficient asymptotic stability bounds were driven by using stability theory of the discrete time-delay system. Results revealed that FOMs with estimated parameters offer systems with different characteristics. Thus, careful consideration must be given when interpreting estimated parameters in FOMs during respiratory tests.