Externally Positive, Passive and Negative Imaginary Systems

The characterisation of externally positive linear systems is considered. These systems are defined by non-negative impulse responses such that their output is positive for positive inputs. The main result shows that if a linear system is both positive real and negative imaginary, then it is externally positive. An LMI condition for external positivity is also proposed by treating the positivity condition as a power. As an application of these results, the optimality of constant current charging for Ii-ion batteries and supercapacitors is obtained by considering them as externally positive systems.