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Robust time‐varying estimator for descriptor system with random one‐step measurement delay

For the linear stochastic descriptor system with random one‐step measurement delay and uncertain‐variance correlated noises, the robust estimation problem is addressed. Applying the singular value decomposition method, augmented state approach and fictitious noise approach, the original descriptor system is transformed to new standard system only with uncertain‐variance fictitious noises. Based on Kalman filtering and the minimax robust estimation principle, the actual Kalman estimator for the proposed standard system with actual measurement and the upper bounds of the variances is presented, including the Kalman predictor, filter, smoother and white noise deconvolution estimator. According to the relation of the new standard system and the original system, the actual estimator of original state of descriptor system and actual estimation error variance are presented. Further, the robustness of the actual estimator is proved by the Lyapunov equation approach, that is, the actual estimation error variance is guaranteed to have minimal upper bound for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.