Transformation of Uncertain Linear Fractional Order Differential Equations Into a Cooperative Form

Abstract

Abstract Occurring uncertainties in dynamical systems can be difficult to handle. A solution can be found in exploiting cooperativity, which avoids the so-called wrapping effect and, hence, simplifies tasks such as the computation of guaranteed state enclosures, the design of interval observers, forecasting worst-case bounds and the identification of unknown parameters. Since not all dynamical systems are originally cooperative, a transformation of the state-space representation has been shown to be effective for ordinary differential equations. However, general approaches are not suitable for fractional order differential equations as they come with different stability regions. This paper shows a control approach for fractional order differential equations and then provides two different methods to transform the derived controlled system models into a cooperative form. The first method is applicable to systems with purely real eigenvalues while the other works for partially conjugate complex ones. Both methods are then validated on a battery system to compare the results and discuss their respective applicability.