A State Space Decomposition Filtering Method for a Class of Discrete-Time Singular Systems

This paper develops a state space decomposition method for a class of discrete-time singular systems. The singular matrix in this system is allowed to vary not only in the value but also in the dimension. An orthogonal factorization is used to rewrite the original space as a direct sum of its two subspaces. Correspondingly, the singular system is replaced by two reduced-order systems, whose states are then calculated respectively. Based on this construction, the prediction of part of the state, optimal filtering result, an optimal one step smoothing result is proposed. Lastly, a numerical example is presented to demonstrate the effectiveness of the new method.