Robust steady-state estimator for descriptor system with uncertain variances, measurement delay and multiplicative noise

The robust estimation problem is addressed for the linear stochastic descriptor system with uncertain variances, random one-step measurement delay and multiplicative noise. By utilizing the singular value decomposition method, fictitious noise method, and augmented state method, the original descriptor system is transformed into a reduced-order standard state space model with only uncertain-variance fictitious noise. Based on the minimax robust estimation principle and Kalman filter theory, the robust steady-state Kalman estimator, which includes the Kalman predictor, filter, smoother, and white noise deconvolution estimator, is presented in the sense that its actual estimation error variance is guaranteed to have the corresponding minimal upper bound for all admissible uncertainties. Additionally, the Lyapunov equation approach proves the robustness of the proposed estimator. An RLC circuit system simulation example shows its effectiveness and correctness.