Robust Kalman Filter Synthesis for Uncertain Multiple Time-Delay Stochastic Systems

Abstract

The problem of robust Kalman filter synthesis is considered in this present study for discrete multiple time-delay stochastic systems with parametric and noise uncertainties. A discrete multiple time-delay uncertain stochastic system can be transformed into another uncertain stochastic system with no delay by properly defining state variables. Minimax theory and Bellman-Gronwall lemma are employed on the basis of the upper norm-bounds of parametric uncertainties and noise uncertainties. A robust criterion can consequently be derived which guarantees the asymptotic stability of the uncertain stochastic system. Designed procedures are finally elaborated upon with an illustrative example.

Quadrature filters for one-step randomly delayed measurements

“…However, the same is not true for randomly delayed measurement problems except a few notable publications on linear systems [18][19][20][21], and nonlinear systems [22][23][24]. The literature on the described problem began with the work of Ray et al, where the authors developed a randomly delayed filtering method for the linear systems.…”

State estimator for multisensor systems with irregular sampling and time-varying delays

“…In that sense, Hsiao and Pan (1996) proposes an extended order model when a reduced constant delay is present. In Larsen et al (1998) the introduction of delayed measurements is dealt with by extrapolating the delayed measurement to the actual instant using the previous estimations of the Kalman filter, and calculating the optimum gain for that extrapolated measurement.…”

Optimal Linear Filtering With State and Observation Delays

“…However, the related optimal filtering problem for linear states with delay has not been solved in a closed form, regarding as a closed form solution a closed system of a finite number of ordinary differential equations for any finite filtering horizon. The optimal filtering problem for time delay systems itself did not receive so much attention as its control counterpart, and most of the research was concentrated on the filtering problems with observation delays (the papers (Alexander, 1991;Hsiao and Pan, 1996;Larsen et al, 1998) could be mentioned to make a reference). A particular case, the optimal filtering problem for linear systems with multiple observation delays, has recently been solved in (Basin and Martinez-Zuniga, 2004).…”