A generalized dynamic robust observer for uncertain linear time invariant descriptor systems. (March 2023) - Jalali, Seyed Mohsen Saeed; Kalat, Ali Akbarzadeh
Abstract: 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. Highlights: A generalized dynamic robust observer for uncertain LTI descriptor systems is designed with a better performance than to PIO/ PO. In the proposed method, it is allowed that parametric uncertainty appears in the derivative, system and input matrices, whiles in the other previous observer, just system or input matrices can contain parametric uncertainty. In the previously presented observers, the system has only uncertain parameters, while in the current study, the coefficient matrices of the system may include unknown or uncertain parameters. In this method, moreover the state variable of the system, the derivatives are also estimated. An LMI form is used to determine sufficient conditions for observer convergence.