Filtering and LQG problems for discrete-time stochastic singular systems

Abstract

Discrete-time stochastic singular systems are discussed. Filtering and linear-quadratic-Gaussian (LQG) problems are considered. The problems are first transformed into the normal form via state augmentation and then solved by utilizing standard results for nonsingular systems. The linear unbiased least-squares state estimation algorithm and the optimal control law for the LQG problem are given. The order of the filtering algorithm obtained in this way is not much increased. Moreover, this algorithm allows the presence of some kinds of control inputs. >