Robust time-varying Kalman predictor for uncertain singular system with missing measurement

For the linear stochastic singular system with missing measurement and uncertain noise variances, the robust Kalman prediction problem is addressed. Applying the singular value decomposition (SVD) method and the fictitious noise approach, the original singular system is transformed to new reduced-order standard system only with uncertain-variance fictitious noises. Applying the minimax robust estimation principle, the minmax robust time-varying 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. Its robustness is proved by the Lyapunov equation approach. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.