How to design externally positive feedback loops – an open problem of control theory

Abstract This paper addresses the properties of externally positive systems and summarises existing conditions and design approaches that achieve externally positive closed-loop dynamics. The output variable of such systems is always nonnegative for any nonnegative input which is a very useful property in various control tasks. This paper investigates the problem of rendering control loops externally positive by an appropriate choice of a feedback. It shows that there is currently no general design procedure for that purpose and the question of when such a controller exists has not been clarified yet. It is also shown that there are plants for which there is no controller that leads to an externally positive control loop.

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