Proportional-Difference Observer Design for Singular Systems in an LMI Framework

Abstract

This paper deals with the problem of proportional-difference observer design for singular systems in the discrete-time domain. Several necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved. Without using any additional transformations, a necessary and sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities. The explicit expression of desired observer is also given. Furthermore, an extension to a class of nonlinear singular systems with Lipschitz constraints is investigated. Finally, a practical example and a numerical one are simulated to illustrate the effectiveness of the proposed approaches.

Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

“…Furthermore, the following assumptions concerning controllability and observability of T-S fuzzy singular systems are proposed. Similar assumptions can be found in [26,33]. In addition, the lemmas are presented to convert stability conditions into LMI form.…”

“…To show the advantages of the proposed design method, the following fuzzy observer and fuzzy controller are established for (33) with a previous design method developed in [23] without considering external disturbance effects.…”

“…These results illustrated the proposed design method's effectiveness and superiority. To show the advantages of the proposed design method, the following fuzzy observer and fuzzy controller are established for (33) with a previous design method developed in [23] without considering external disturbance effects. The comparisons of state responses and estimation errors are shown in Figures 3 and 4, respectively.…”

“…The related PD control problems were studied in [27][28][29][30][31][32]. The PD observer issue for discrete-time singular systems was studied in [33]. In [25,26], the stabilization via PD state feedback fuzzy control scheme was studied.…”