Robust steady-state Kalman filter for descriptor system with random one-step measurement delays and uncertain noise variances

For the linear stochastic descriptor system with random one-step measurement delays and uncertain noise variances, the robust steady-state Kalman predictor is addressed. By new augmented state approach, the original system is transformed to the standard systems without measurement delays. The singular value decomposition (SVD) method, the randomization approach and the augmented state approach are presented, which are applied to transform the descriptor system with random one-step measurement delay to the standard non-descriptor system with fictitious white noises. Applying the presented approaches, the minimax robust steady-state Kalman predictor is presented in the sense that its actual prediction error variance is guaranteed to have the corresponding minimal upper bound for all admissible uncertainties. Their robustness is proved by the Lyapunov equation approach. A simulation example about circuits system verifies the correctness of the proposed results.