On Second-Order Cone Positive Systems

Internal positivity offers a computationally cheap certificate for external (input-output) of linear time-invariant system. However, the drawback with this lies in its realization dependency. First, computing such requires finding polyhedral cone potentially high number extremal generators that lifts dimension state-space representation, significantly. Second, not all externally positive systems possess an internally realization. Third, many typical applications as controller design, system identification, and model order reduction, internal is preserved. To overcome these drawbacks, we present tractable sufficient based on second-order cones. This does require any special realization: if it succeeds possibly non-minimal realization, then will do so minimal While there exist where also necessary, demonstrate how to construct systems, both cones well other certificates fail. Nonetheless, contrast independent certificates, second-order-cone one appears be favorable terms applicability conservatism. Three are representatively discussed underline potential. We show can used find approximations nearly may help reduce identification errors. The same algorithm design state-feedback controllers provide closed-loop positivity, common approach avoid over- undershooting step response. Last, modifications generalized balanced truncation preserved those our applies.