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Authors
Canudas de Wit, Carlos, Ramos Cueli, José

Identifier
10.3182/20080706-5-KR-1001.01739

Index Terms
Networked embedded control systems; Control over networks; Control over communication

Abstract
This paper presents a constructive algorithm to design local controllers for feedback systems that are interconnected via time-varying and asynchronous sampling. These systems result in many application fields such as remotely-operated systems, interconnected vehicle control loops, and more generally in component-based control design where synchronous exchange of information is not feasible. The design is based on the (MASP) emph{MAximum Sampling time preserving Passivity}, and uses discrete-time passivity considerations. The paper first explores several ways to compute the MASP for linear systems, and then proposes a numerical algorithm to compute local feedback loops providing a MASP compatible with the maximum sampling-time upperbound of each sub-system. This results in a exponentially stable interconnection. The paper also presents a simulation example of this design.

References

M. Araki. Recent development in digital control theory. In
Proc. of the 12th IFAC World Congr., volume 9, pages
951{960, 1993.
B. Brogliato, R. Lozano, O. Egeland, and B. Maschke.
Dissipative Systems Analysis and Control. Theory and
Applications. Springer-Verlag, London, second edition,
2007.
L. El-Ghaoui and S.-I. Niculescu, editors. Advances in
Linear Matrix Inequality Methods in Control. Advances
in Design and Control. SIAM, Philadelphia, 2000.
D.A. Harville. Matrix Algebra from a Statiscian's Perspec-
tive. Springer-Verlag, New York, 1997.
A. Hassibi, S.P. Boyd, and J.P. How. Control of asyn-
chronous dynamical systems with rate constraints on
events. Stanford University, 1999.
P.F. Hokayem and M.W. Spong. Bilateral teleoperation:
An historical survey. Automatica, December 2006.
D.S. Laila, D. Nesic, and A.R. Teel. Open and closed loop
dissipation inequalities under sampling and controller
emulation. April 2001.
H. J. M�arquez. Nonlinear Control Systems: Analysis and
Design. Wiley-Interscience, May 2003.
P. Marti, R. Villa, G. Fohler, and J.M. Fuertes. A
discrete-time controller design method to tolerate
non-equidistant sampling and actuation. Technical
report, Automatic Control Department. Universidad
Polit�ecnica de Catalu~na, January 2002. ESAII-RR-02-
05.
R.-M. Murray, K.-J. Astrom, S.P. Boyd, R.W. Brock-
ett, and G. Stein. Future directions in control in an
information-rich word. IEEE Control System magazine,
April 2003.
E.M. Navarro-Lopez. Several dissipativity and passivity
implications in the linear discrete time-setting. Mathe-
matical Problems in Engineering, 6:599{616, 2005.
E.M. Navarro-Lopez. Dissipativy and Passivity-related
Properties in Nonlinear Discrete Time Systems. PhD
thesis, Universidad Politecnica de Catalu~na, 2002. Insti-
tuto de Organizacion y Control de Sistemas Industriales.
J. Nilsson and B. Bernhardsson. LQG control over a
Markov communication network. Lund Institute of
Technology, 1997.
A. Rantzer and C.I. Byrnes, editors. Directions in Mathe-
matical Systems Theory and Optimization, chapter Sys-
tems with Lebesgue Sampling, pages 1{13. Springer-
Verlag, Berlin, 2003.
D. Robert. Contribution �a l'interaction com-
mande/ordonnancement. PhD thesis, Institut National
Polytechnique de Grenoble, Laboratoire d'Automatique
de Grenoble - Ecole de l'Energie et du Traitement de
l'Information, January 2007.
R.A. Rohrer and H. Nosrati. Passivity considerations
in stability studies of numerical integration algorithms.
IEEE Transactions on Circuits and Systems, CAS-28
(9):857{866, September 1981.