Optimal Estimation of A Class of Linear Time‐Delay Uncertain Systems

Abstract

The state estimation problem is investigated for a class of linear uncertain systems with state and noise delay. The optimal one-step prediction algorithm is presented by introducing a fictitious noise. The predictor is designed based on the projection formula in Hilbert space and has the same dimensions as the original systems. The error covariance consists of two coupled Riccati-type difference equations. The optimal filter and fixed-lag smoother are provided based on the predictor. A numerical example is given to show the effectiveness of the proposed approach.

Design of Full‐Order Observers for Systems with Unknown Inputs by Using the Eigenstructure Assignment

“…Disturbances are called unknown inputs if they affect the process input, their presence making difficult the state estimation [13]. The state estimation problem for linear multivariable system, subjected to unknown inputs, has received considerable attention in recent decades [10,[14][15][16][17][18]. The dimension of the observer is considerably increased in [13] and that is why the approach of Wang et al [14] is more interesting; they proposed a method to design reduced-order observers without any knowledge of these inputs; existence conditions for this observer have been provided by Kudva et al [15].…”

“…Disturbances are called unknown inputs if they affect the process input, their presence making difficult the state estimation . The state estimation problem for linear multivariable system, subjected to unknown inputs, has received considerable attention in recent decades . The dimension of the observer is considerably increased in and that is why the approach of Wang et al .…”

State estimation for stochastic time‐varying multisensor systems with multiplicative noises: Centralized and decentralized data fusion

“…A suboptimal weighted filter based on local Kalman filters for systems with unknown parameters is presented in . In , state estimation methods are presented for linear and nonlinear systems with multiplicative noises, respectively. A distributed robust filter for linear systems subjected to stochastic uncertainties is presented in .…”

Adaptive Robust Output Tracking Control of Uncertain Nonlinear Cascade Systems with Disturbance and Multiple Unknown Time‐Varying Delays

“…In practical control problems, external disturbance, parameter uncertainty, and time‐varying delay exist in many engineering systems. Since time delay and uncertainties may be sources of instability in many dynamical systems, considerable attention has been devoted to the problem of stability analysis and control of such systems . Linear uncertain time delay systems have been intensively investigated in previous studies .…”

“…Since time delay and uncertainties may be sources of instability in many dynamical systems, considerable attention has been devoted to the problem of stability analysis and control of such systems . Linear uncertain time delay systems have been intensively investigated in previous studies . A significant difficulty in the control of delayed systems is that the delays are usually unknown and time‐varying.…”