Positive systems[1][2] constitute a class of systems that has the important property that its state variables are never negative, given a positive initial state.
These systems appear frequently in practical applications,[3][4] as these variables represent physical quantities, with positive sign (levels, heights, concentrations, etc.).
The fact that a system is positive has important implications in the control system design.
[5] For instance, an asymptotically stable positive linear time-invariant system always admits a diagonal quadratic Lyapunov function, which makes these systems more numerical tractable in the context of Lyapunov analysis.
[6] It is also important to take this positivity into account for state observer design, as standard observers (for example Luenberger observers) might give illogical negative values.