A robust filtering framework for uncertain descriptor systems with unknown inputs and missing measurements

This paper addresses robust state estimation problem for uncertain descriptor systems subject to norm bounded uncertainties, arbitrary unknown inputs, and probabilistic missing measurements which are described by a Bernoulli distributed white sequence. A system reformation based robust filtering framework (SRRFF) is proposed based on the recently developed signal division method (SDM), intending to reform the uncertain system into a corresponding nominal system. Through the SRRFF, it is shown in this paper that the state estimation for an uncertain system can be recast into one that is for an equivalent nominal system (ENS). In the sequel, with the aid of the ENS, existing unbiased minimum-variance filters can be easily applied to achieve the optimal robust state estimation. This research shows that the robust state estimation problem can be treated with a stochastic formulation approach, the same as the Kalman filtering, other than the well-known regularized least-squares (RLS) problem.