A generalized dynamic robust observer for uncertain linear time invariant descriptor systems

This paper presents a generalized dynamic robust observer design for uncertain linear time-invariant (LTI) singular systems. In this approach, the state equation of the singular system can consist of parametric uncertainties in three matrices namely the derivative, the system, and the input. The proposed method is according to a new parameterization in the system equations and converting it to a new descriptor model so that in the new structure, the derivative matrix is known. A generalized dynamic robust observer is suggested to estimate the state variables of the system which has more flexibility in contrast with proportional and proportional-integral observers. Also, in this method, in addition to the state variables, whose derivatives are also estimated. A sufficient condition is given in a linear matrix inequality (LMI) form to show the convergence of the observer. Numerical simulation demonstrates the efficacy of the proposed observer.