Monotone nonlinear realisations of response maps

ABSTRACT

The problem of realisation of a monotone response map as a monotone initialised system on a finite dimensional Euclidean state space is investigated. The dynamical part of the system is described by a delta differential equation on an arbitrary time scale. This incorporates continuous- and discrete-time systems. The main result states necessary and sufficient conditions for existence of a monotone realisation of a particular class. The criterion is expressed in the language of skew differential global universes.

KEYWORDS:

• Monotone system
• response map
• realisation
• time scale
• global universe

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Science Centre [grant number 2013/09/B/ST7/04216].