Robust time-varying Kalman predictor for descriptor system with random one-step measurement delay and multiplicative noise

For the linear stochastic descriptor system with random one-step measurement delay and multiplicative noise, the robust prediction problem is addressed. Applying the singular value decomposition (SVD) method, 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 time-varying Kalman predictor is presented by replacing the unrealization conservative measurement by the actual measurement in the conservative Kalman predictor. Further, the robustness is proved by the Lyapunov equation approach, i.e., the actual estimation error variance are 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.