Mohamed Darouach

Full-order observers for linear systems with unknown inputs

This note presents a simple method to design a full-order observer for linear systems with unknown inputs. The necessary and sufficient conditions for the existence of the observer are given. >

Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems

In this paper, convergence analysis of the extended Kalman filter (EKF), when used as an observer for nonlinear deterministic discrete-time systems, is presented. Based on a new formulation of the first-order linearization technique, sufficient conditions to ensure local asymptotic convergence are established. Furthermore, it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified EKF significantly. The efficiency of this approach, compared to the classical version of the EKF, is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete-time systems.

Unbiased minimum variance estimation for systems with unknown exogenous inputs

A new method is developed for the state estimation of linear discrete-time stochastic systems in the presence of an unknown disturbance. The filter obtained is optimal in the unbiased minimum variance sense. The necessary and sufficient conditions for the existence and the stability of the filter are given.

Reduced-order observer design for descriptor systems with unknown inputs

A new method for the design of reduced-order observers for descriptor systems with unknown inputs is presented. The approach is based on the generalized constrained Sylvester equation. Sufficient conditions for the existence of the observer are given.

Existence and design of functional observers for linear systems

This paper presents straightforward derivations of the functional observers design for linear time-invariant multivariable systems. The order of these observers is equal to the dimension /spl tau/ of the vector to be estimated. Necessary and sufficient conditions for the existence and stability of these observers are given. Illustrative examples are included.

Linear functional observers for systems with delays in state variables

This paper is concerned with the design of linear functional state observers for systems with delays in state variables. In particular, the necessary and sufficient conditions for the existence of the rth-order observers are given. Sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix-in-equality formulation. A systematic design method of these observers is presented. Numerical examples are given to illustrate this method.

Brief Extension of minimum variance estimation for systems with unknown inputs

In this paper, we address the problem of minimum variance estimation for discrete-time time-varying stochastic systems with unknown inputs. The objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs. It extends the results of Darouach and Zasadzinski (Automatica 33 (1997) 717) where the unknown inputs are only present in the model. The main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises, this fact leads generally to suboptimal filters. Necessary and sufficient conditions for the unbiasedness of this filter are established. Then conditions under which the estimation error and the system noises are uncorrelated are presented, and an optimal estimator and a predictor filters are derived. Sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time-invariant case. A numerical example is given in order to illustrate the proposed method.

State estimation of stochastic singular linear systems

Abstract This simple algorithm for the state estimation of stochastic singular linear systems is based on the least squares method.

Kalman filtering with unknown inputs via optimal state estimation of singular systems

A new method for designing a Kalman filter for linear discrete-time systems with unkown inputs is presented. The algorithm recently developed for stochastic singular systems is applied to obtain a linear estimation of the state and unkown inputs. The necessary and sufficient conditions for the existence and stability of the filter are derived and proved. An illustrative example is included.

Optimal two-stage Kalman filter in the presence of random bias

This paper gives an optimal solution of the two-stage Kalman filter for linear stochastic systems subject to random bias. It is shown that the state estimate can be expressed as xkk = xkk + βkkbkk where xkk is a modified bias-free state estimate and bkk the optimal estimate of random bias.