Robust steady-state Kalman filter for uncertain descriptor system with missing measurement and uncertain-variance correlated noises

For the linear stochastic descriptor system with missing measurement and uncertain-variance correlated noise, the robust steady-state Kalman filtering problem is addressed. Applying the singular value decomposition (SVD) method and the fictitious noise approach, the original uncertain descriptor system is transformed to new reduced-order standard system only with uncertain-variance fictitious noises. Applying the minimax robust estimation principle and classical Kalman filtering theory, the actual steady-state Kalman filter is presented in the sense that its actual filtering error variance is guaranteed to have the corresponding minimal upper bound for all admissible uncertainties. Applying the Lyapunov equation approach, the robustness of the presented actual steady-state Kalman filter is proved, which is also called as the robust steady-state Kalman filter. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.