The state space model of the scalar, fractional order, variable parameters dynamic system

Abstract

In the paper the new, discrete, variable parameters, scalar, fractional order state space model is addressed. The proposed model uses Fractional Order Backward Difference approximation with linearly time varying parameters: fractional order and quasi-time constant. Elementary properties of the considered model: practical stability, accuracy and positivity are discussed. Theoretical considerations are illustrated by numerical tests. The proposed model can be applied to the modeling of physical phenomena hard to describe with the use of time invariant approach.