Functional Observers For Linear Systems Research Articles

Some new standpoints in the design of asymptotic functional linear observers

The owl of Minerva spreads its wing only with the falling of the dusk. The aim of this work is to provide some new trends in the observation for linear systems. In the general framework of designing linear functional observers for linear systems the necessary and sufficient existence conditions are well known. Whether in the O'Reilly textbook or in the recently published ones on this topic, and, roughly speaking, the design methods can be categorized in two kinds. The first one is based on the solution of a Sylvester equation and a projection of the observed linear functional. The second one, based on the recent notion of functional observability, starts from the Darouach criterion which is an Popov-Belevitch-Hautus type one. Nevertheless, the main drawback of the deduced methods is that they cannot be used for linear time-varying systems. These models are of primary importance, for instance with linearization about a trajectory. Consequently, we cope with this problem by considering a new point of view for the design of linear functional observers. We see also that Darouach observers or Cumming-Gopinath observers are particular cases of the proposed methodology. For simplicity sake we suppose the system has no unknown inputs and is not described by a distributed parameters model as well. Nevertheless, these cases can be thought as possible extensions of the presented standpoints.

On functional observers for linear systems with unknown inputs and HOSM differentiators

The problem of constructing functional observers for linear systems with unknown inputs is considered. Necessary and sufficient conditions for the existence of a proper observer (without differentiations) are revisited. A simple and explicit form of a functional observer is presented. It is shown that when such observer is not proper, it is still possible to use the High-Order Sliding Mode differentiator to implement it. Nevertheless, in such case, additional conditions on the system and the unknown input are required.

Impulsive functional observers for linear systems

The problem of designing functional observers for linear impulsive systems is addressed. By applying suitable matrix transformations, sufficient conditions for the existence of the functional observers that are capable of exponentially estimating any given function of the state vector are derived. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

On Functional Observers for Linear Systems with Unknown Inputs and HOSM Differentiators

AbstractFunctional observers for linear systems with unknown inputs are studied. Necessary and sufficient conditions for the existence of a proper observer (without differentiations) are revisited. It is shown that when the observer is not proper, it is still possible to use the HOSM differentiator to construct an observer for systems with a known upper bound of the unknown input, with theoretically exact convergence.

Minimal single linear functional observers for linear systems

A constructive procedure to design a single linear functional observer for a time-invariant linear system is given. The proposed procedure is simple and is not based on the solution of a Sylvester equation or on the use of canonical state space forms. Both stable observers or fixed poles observers problems are considered for minimality.

Time-Delay Systems: Design of Delay-Free and Low-Order Observers

This note provides a comprehensive treatment on the design of functional observers for linear systems having a time-varying delay in the state variables. The designed observers possess attractive features of being low-order and delay-free and hence they are cost effective and easy to implement. Existence conditions are derived and a design procedure for finding low-order observers is given.

Disturbance Decoupled Observers for Systems With Unknown Inputs

This note deals with the design of reduced-order disturbance decoupled scalar functional observers for linear systems with unknown inputs. Based on a parametric approach, existence conditions are derived and a design procedure for finding reduced-order scalar functional observers is given. The derived existence conditions are relaxed and the procedure can find first-order disturbance decoupled scalar functional observers for some cases where the number of unknown inputs is more than the number of outputs. Also, the observer matching condition, which is the necessary requirement for the design of state observers for linear systems with unknown inputs, is not required. Numerical examples are given to illustrate the attractiveness of the proposed design method.

FUNCTIONAL OBSERVERS FOR LINEAR SYSTEMS WITH UNKNOWN INPUTS

ABSTRACTIn this paper, a straightforward approach is presented to design functional observers for linear systems with unknown inputs. Necessary and sufficient conditions are provided for the existence of the observers. Some illustrated examples are included.

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.

Design of linear functional observers for linear systems with unknown inputs

This paper presents a reduced-order linear functional state observer for linear systems with unknown inputs. A simple observer construction procedure is provided. A numerical example is given to illustrate the properties of the observer. The example deals with a linear system comprising of 20 states, 2 inputs, 10 outputs and 5 unknown inputs for which a fourth-order observer is designed to estimate two linear functions of the states.

Reduced-order linear functional observer for linear systems

A new reduced-order linear functional observer is introduced in this paper. The order of the observer is proportional to the ratio of the number of output measurements to the number of inputs. It is shown that the observer asymptotically converges to any number of linear functionals when some minor conditions are met. A simple observer construction procedure, which is easy to implement on MATLAB, is provided. Numerical examples are considered to illustrate the properties of the observer.

Functional observers for linear systems with unknown inputs

This paper addresses the problem of designing an observer capable of estimating linearly independent functions of state variables of a linear system that is driven by both known and unknown inputs. Necessary and sufficient conditions for the existence of the observer, referred to as functional unknown input observer (FUIO) is provided in this article. Furthermore, a constructive design approach based on some results in loop transfer recovery theory is presented.