Some Observability Conditions for a Fractional order Descriptor System; A new Approach

Abstract

In this article, a descriptor systems involving singular and non-singular matrix $E_{n\times n}$ in the both input and output equation for the observability condition has been studied. The discussion is for both classical order derivative and Caputo's fractional order derivative.Firstly, the solution is obtained and further the observability conditions in form of Grammian matrices and rank conditions as per Kalman criteria are verified. These results are more generalized and can be verified for various special cases in the observability results for various types of descriptor systems.