State and Unknown Inputs Estimations for Multi-Models Descriptor Systems

In this note, the problem of states and unknown inputs estimation of nonlinear descriptor system is considered. The methodology is based on the use of Proportional Integral and Unknown Input Observers. The considered nonlinear descriptor system is transformed into an equivalent multi-models form by using the Takagi-Sugeno (T-S) approach. In this paper, the design methods of both proportional integral observers and unknown inputs observers for descriptor multi-models are described in detail. Sufficient conditions of stability analysis and gain matrices determination are performed by resolving a set of Linear Matrices Inequalities (LMIs). The design method offers all the degrees of design freedom, which can be utilized to achieve various desired system specifications and performances and, thus, has great potentials in applications. A numerical example is employed to show the design procedure of these two observers and illustrate the effect of the proposed approach.