We compute explicitly feedback linearizing coordinates for a two-input control system without solving the corresponding PDEs. Our algorithm is based on a successive application of the Frobenius’ theorem and does not necessitate the checking of the involutive conditions for feedback linearization. Examples are provided for illustration.

Issue Section:
Technical Briefs
Topics:
Algorithms, Control systems, Feedback, Theorems (Mathematics)

References

1.
Brockett
,
R. W.
, 1978, “
Feedback Invariants for Nonlinear Systems
,”
Proceedings of the IFAC
, Helsinski, Sweden.
2.
Hunt
,
L. R.
, and
Su
,
R.
, 1981, “
Linear Equivalents of Nonlinear Time Varying Systems
,”
Proceedings of the Mathematical Theory of Networks and Systems
, CA, USA, pp.
119
–
123
.
3.
Jakubczyk
,
B.
, and
Respondek
,
W.
, 1980, “
On Linearization of Control Systems
,”
Bull. Acad. Polon. Sci. Ser. Math.
,
28
, pp.
517
–
522
.
4.
Krener
,
A. J.
, 1973, “
On the Equivalence of Control Systems and the Linearization of Nonlinear Systems
,”
SIAM J. Control
,
11
, pp.
670
–
676
.
Crossref
Search ADS
 
5.
Mullhaupt
,
Ph.
, 2006, “
Quotient Submanifolds for Static Feedback Linearization
,”
Syst. Control Lett.
,
55
, pp.
549
–
557
.
Crossref
Search ADS
 
6.
Onawola
,
O. O.
, and
Sinha
,
S. C.
, 2011, “
A Feedback Linearization Approach for Panel Flutter Suppression with Piezoelectric Actuation
,”
J. Comput. Nonlinear Dyn.
,
6
(
1
), pp.
1
–
8
.
7.
Tall
,
I. A.
, 2009, “
State Linearization of Control Systems: An explicit Algorithm
,”
Proceedings of the Joint 48th IEEE CDC and 28th CCC Conference
, Shanghai, P. R. C., pp.
7448
–
7453
.
8.
Tall
,
I. A.
, 2009, “
Explicit Feedback Linearization of Control Systems
,”
Proceedings of the Joint 48th IEEE CDC and 28th CCC Conference
, Shanghai, P. R. C., pp.
7454
–
7459
.
9.
Tall
,
I. A.
, 2010, “
State and Feedback Linearizations of Single-Input Control Systems
,”
Syst. Control Lett.
,
59
, pp.
429
–
441
.
Crossref
Search ADS
 
10.
Zhang
,
Y.
, and
Sinha
,
S. C.
, 2007, “
Development of a Feedback Linearization Technique for Parametrically Excited Nonlinear Systems via Normal Forms
,”
J. Comput. Nonlinear Dyn.
, pp.
124
–
131
.
11.
Tall
,
I. A.
, 2010, “
Multi-Input Control Systems: Feedback Linearization
,”
Proccedings of the 49th IEEE CDC10
,
Atlanta, GA, USA
.
12.
Tall
,
I. A.
, 2011, “
Flow Box Theorem and Beyond
,”
Afr. Diaspora J. Math.
,
11
(
1
), pp.
75
–
102
.
13.
Nijmeijer
,
H.
, and
van der Schaft
,
A. J.
, 1990,
Nonlinear Dynamical Control Systems
,
Springer-Verlag
,
New York
.
14.
Serrani
,
A.
,
Isidori
,
A.
,
Byrnes
,
C. I.
, and
Marconi
,
L.
, 2000, “
Recent Advances in Output Regulation of Nonlinear Systems
,”
Nonlinear Control in the Year 2000
,
A.
Isidori
,
F.
Lamnabhi-Lagarrigue
, and
W.
Respondek
, eds.,
LNCIS
, Vol.
259
, pp.
409
–
419
.
Copyright © 2012
 by American Society of Mechanical Engineers
You do not currently have access to this content.