On the convergence and stability of fractional singular Kalman filter and Riccati equation

In our recent paper [1], we have developed a simple algorithm for the state estimation of discrete-time linear stochastic fractional-order singular (FOS) systems based on the deterministic least squares method. In this paper, we shall consider the asymptotic properties of the obtained generalized Riccati equation and the associated state estimator. The approach is based on the analysis in detail of the derived filter and algebraic Riccati equation by generalizing significantly the results for standard causal systems, in which provide us conditions for the stability and convergence of the fractional singular Kalman filter (FSKF). Also, conditions under which the Riccati equation has a unique positive semi-definite (PSD) solution are given. Towards this, stability studies of discrete-time FOS state-space systems are investigated, and detectability and stabilizability criterions have been derived. Some examples are performed and verified using numerical simulations in order to illustrate the given analysis. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.