Tuning regulators for tracking SISO positive linear systems

The importance that positive linear systems play in applications is overwhelming; however, to date there appears to be no study of the servomechanism problem for such systems. We consider the tracking problem of nonnegative constant reference signals for unknown stable SISO positive linear systems with nonnegative constant disturbances. In particular, we are interested in the application of tuning regulators to the tracking problem. The results presented in this paper show that any unknown stable SISO positive linear system initially at rest can track any nonnegative constant reference signal while maintaining nonnegativity of the states and outputs with a nonnegative control input. Additionally, we show that almost state nonnegativity and tracking of nonnegative constant references is achievable for unknown stable SISO positive linear systems under nonnegative disturbances and arbitrary nonnegative initial conditions.