This paper presents a new strategy for state estimation. The strategy may be applied to linear systems and is referred to as the variable structure filter. The filter is considered for discrete-time systems subject to random disturbances and measurement noise. It requires a parametric model and can be formulated to accommodate modeling uncertainties. A proof of stability for the filter is provided. For stability, this concept requires a specification of an upper bound for uncertainties, disturbances, and measurement noise. The application of this filter to a third-order linear system is demonstrated.

1.
Kalman
,
R.E.
,
1960
, “
A New Approach to Linear Filtering and Prediction Problems
,”
ASME J. Basic Eng.
,
82
,
35
45
.
2.
Brown, R.G., and Hwang, P.Y.C., 1997, “Introduction to Random Signals and Applied Kalman Filtering,” Third Edition, Wiley, New York.
3.
Horton
,
M.P.
, 1997, “Real-Time Identification of Missile Aerodynamics using Linearized Kalman Filter Aided by an Artificial Neural Network,” IEE Proc.: Control Theory Appl., 144.
4.
Sorenson
,
H.W.
,
1970
, “
Least-Squares Estimation: From Gauss to Kalman
,”
IEEE Spectrum
,
7
, pp.
63
68
.
5.
Grewal, M.S., and Andews, A.P., 1993, “Kalman Filtering Theory and Practice,” Prentice-Hall, Englewood Cliffs, NJ.
6.
Elbert, T.F., 1984, “Estimation and Control of Systems,” Van Nostrand Reinhold Company.
7.
Utkin
,
V.I.
,
1977
, “
Variable Structure Systems with Sliding Mode: A Survey
,”
IEEE Trans. Autom. Control
,
AC-22
, pp.
212
222
.
8.
Utkin, V.I., 1978, “Sliding Mode and Their Application in Variable Structure Systems,” English translation, Mir Publication, Moscow.
9.
Ryan
,
E.P.
, and
Corless
,
M.
,
1984
, “
Ultimate Boundedness and Asymptotic Stability of a Class of Uncertain Dynamical Systems via Continuous and Discontinuous Feedback Control
,”
J. Math. Control and Information
,
1
, pp.
223
242
.
10.
Morgan
,
R.G.
, and
Ozguner
,
U.
, 1985, “A Decentralised Variable Structure Control Algorithm for Robotic Manipulators,” IEEE J. Rob. Autom., RA-1.
11.
Yeung
,
K.S.
, and
Chen
,
V.P.
,
1988
, “
A New Controller Design for Manipulators using the Theory of Variable Structure Systems
,”
IEEE Trans. Autom. Control
,
33
, pp.
200
206
.
12.
Habibi
,
S.R.
, and
Richards
,
R.J.
,
1992
, “
Sliding Mode Control of an Electrically Powered Industrial Robot
,”
IEE Proc.-D: Control Theory Appl.
,
139
, pp.
207
225
.
13.
Asada, H., and Slotine, J.J.E., 1986, Robot Analysis and Control, John Wiley Publications, New York.
14.
Bailey
,
E.
, and
Arapostathis
,
A.
,
1987
, “
Simple Sliding Mode Control Scheme Applied to Robot Manipulators
,”
Int. J. Control
,
45
, pp.
1197
1209
.
15.
Slotine
,
J.J.E.
,
1984
, “
Sliding Controller Design for Nonlinear Systems
,”
Int. J. Control
,
40
, pp.
421
434
.
16.
Slotine
,
J.J.E.
,
1985
, “
The Robust Control of Robot Manipulators
,”
Int. J. Robot. Res.
,
4
, pp.
49
64
.
17.
Slotine
,
J.J.E.
, and
Coetsee
,
J.A.
,
1986
, “
Adaptive Sliding Mode Control Synthesis for Nonlinear Systems
,”
Int. J. Control
,
43
, pp.
1631
1651
.
18.
Buhler, H., 1986, “Reglage par Mode de Glissement,” Press Polytechnique Romande.
19.
Slotine
,
J.J.E.
,
Hedrick
,
J.K.
, and
Misawa
,
E.A.
,
1987
, “
On Sliding Observers for Nonlinear Systems
,”
J. Dyn. Syst., Meas., Control
,
109
, pp.
245
252
.
20.
Walcott
,
B.L.
, and
Zak
,
S.H.
,
1988
, “
Combined Observer-Controller Synthesis for Uncertain Dynamical Systems with Applications
,”
IEEE Trans. Syst. Man Cybern.
,
108
, pp.
88
104
.
21.
Edwards
,
C.
, and
Spurgeon
,
S.K.
,
1994
, “
On the Development of Discontinuous Observers
,”
Int. J. Control
,
59
, pp.
1211
1229
.
22.
Xu
,
J.X.
,
Jia
,
Q.W.
, and
Lee
,
T.H.
,
2000
, “
On the Design of a Nonlinear Adaptive Variable Structure Derivative Estimator
,”
IEEE Trans. Autom. Control
,
45
, pp.
1028
1033
.
23.
Nise, N.S., 2000, “Control Systems Engineering,” Wiley, New York, Third Edition.
24.
Habibi
,
S.R.
, and
Singh
,
G.
,
2000
, “
Derivation of Design Requirements for Optimization of a High Performance Hydrostatic Actuation System
,”
International Journal of Fluid Power
,
1
, pp.
11
27
.
25.
Habibi
,
S.R.
, and
Goldenberg
,
A.A.
,
2000
, “
Design of a New High Performance ElectroHydraulic Actuator
,”
IEEE Trans. on Mechatronics
,
5
, pp.
158
164
.
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