This paper presents a design technique for the synthesis of robust observers for linear dynamical systems with uncertain parameters. The perturbations under consideration are modelled as unknown but bounded disturbances and an ellipsoidal set-theoretic approach is used to formulate the optimal-observer design problem. The optimal criterion introduced here is the minimization of the ‘size’ of the bounding ellipsoid of the estimation error. A necessary and sufficient condition for this optimal design problem is presented. The results are stated in terms of a reduced-order observer with constant gain matrix, which is then determined by solving a matrix Riccati-type equation. Furthermore, a gradient-search algorithm is presented to find the optimal solution when the free parameter that enters in the construction of the bounding ellipsoids of the estimation error is considered as a design parameter. The effectiveness of the proposed approach is illustrated through a numerical example.
[1]
John O'Reilly,et al.
Observers for Linear Systems
,
1983
.
[2]
Fred C. Schweppe,et al.
Uncertain dynamic systems
,
1973
.
[3]
G. Golub,et al.
A Hessenberg-Schur method for the problem AX + XB= C
,
1979
.
[4]
R. Stefani.
Observer steady-state errors induced by errors in realization
,
1976
.
[5]
Brian D. O. Anderson,et al.
Linear Optimal Control
,
1971
.
[6]
Katsuhisa Furuta,et al.
A class of systems with the same observer
,
1976
.
[7]
D. Luenberger.
Observers for multivariable systems
,
1966
.
[8]
J. J. Bongiorno,et al.
On the design of observers for insensitivity to plant parameter variations
,
1973
.
[9]
B. Gopinath.
On the control of linear multiple input-output systems
,
1971
.
[10]
S. Bhattacharyya.
Parameter invariant observers
,
1980
.