Robust steady-state Kalman filter for descriptor system with uncertain-variance noise and packet dropout

For the linear stochastic descriptor system with packet dropout and uncertain-variance noises, the robust steady-state filtering problem is addressed. Applying the singular value decomposition (SVD) approach, augmented state approach and the fictitious noise approach, the original descriptor system is transformed to new standard system only with uncertain-variance fictitious noises. Based on Kalman filtering and minimax robust estimation principle, the robust steady-state Kalman filter is presented by replacing the unrealization conservative measurement by the actual measurement in the conservative steady-state Kalman filter. Further, the robustness is proved by the Lyapunov equation approach, i.e., the actual filtering error variance is guaranteed to have minimal upper bounds for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.