Robust time-varying Kalman predictor for descriptor system with random one-step measurement delays

For the linear stochastic descriptor system with random one-step measurement delays and uncertain noise variances, the robust time-varying Kalman prediction problem is addressed. 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 and uncertain noise variances to the standard non-descriptor system only with fictitious uncertain-variance white noises. For this standard non-descriptor system, the minimax robust time-varying Kalman predictor is presented based on the minimax robust estimation principle 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.