» Download Article

Authors
Forni, Fulvio; Nesic, Dragan; Zaccarian, Luca

Digital Object Identifier (DOI)
10.3182/20100901-3-IT-2016.00203

Page Numbers:
617-622

Index Terms
Hybrid Nonlinear Control Systems; Passivity; I/O Stability

Abstract
For a class of square continuous time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule, we prove that the arising hybrid system with temporal regularization is passive in the conventional continuous time sense with a small shortage of input passivity decreasing with the temporal regularization constant. Based on the passivity property, we then investigate the finite gain stability of the interconnection between this passive controller and a passive nonlinear plant.

References

REFERENCES

Beker, O., C.V. Hollot and Y. Chait (2001). Plant with
an integrator: an example of reset control overcoming
limitations of linear feedback. IEEE Transac-
tions Automatic Control 46, 1797–1799.

Beker, O., C.V. Hollot, Y. Chait and H. Han (2004).
Fundamental properties of reset control systems.
Automatica 40, 905–915.

Cai, C. and A.R. Teel (2009). Characterizations of inputto-
state stability for hybrid systems. Systems &
Control Letters 58(1), 47–53.

Carrasco, J., A. Banos and A. Van der Schaft (2010).
A passivity-based approach to reset control systems
stability. Systems & Control Letters 59(1), 18–24.
Clegg, J.C. (1958). A nonlinear integrator for servomechanisms.
Trans. A. I. E. E. 77 (Part II), 41–42.

Collins, P. (2004). A trajectory-space approach to hybrid
systems. In: International Symposium on the Math-
ematical Theory of Networks and Systems. Leuven,
Belgium.

Fantoni, I., R. Lozano and M.W. Spong (2000). Energy
based control of the pendubot. Automatic Control,
IEEE Transactions on 45(4), 725–729.

Goebel, R. and A.R. Teel (2006). Solutions to hybrid
inclusions via set and graphical convergence with
stability theory applications. Automatica 42(4), 573
– 587.

Goebel, R., R. Sanfelice and A.R. Teel (2009). Hybrid dynamical
systems. Control Systems Magazine, IEEE
29(2), 28–93.

Horowitz, I. and P. Rosenbaum (1975). Non-linear design
for cost of feedback reduction in systems with large
parameter uncertainty. Int. J. Contr 21, 977–1001.

Johansson, K.H., J. Lygeros, S. Sastry and M. Egerstedt
(1999). Simulation of Zeno hybrid automata. In:
Conference on Decision and Control. Phoenix, Arizona.
pp. 3538–3543.

Khalil, H.K. (2002). Nonlinear Systems. 3rd ed.. Prentice
Hall. USA.

Morabito, F., S. Nicosia, A.R. Teel and L. Zaccarian
(2004). Measuring and improving performance
in anti-windup laws for robot manipulators. In:
Advances in Control of Articulated and Mobile
Robots (B. Siciliano, A. De Luca, C. Melchiorri and
G. Casalino, Eds.). Chap. 3, pp. 61–85. Springer
Tracts in Advanced Robotics.

Neˇsi´c, D., L. Zaccarian and A.R. Teel (2008). Stability
properties of reset systems. Automatica (B)
44(8), 2019–2026.

van der Schaft, A. (1999). L2-Gain and Passivity in
Nonlinear Control. second ed.. Springer-Verlag New
York, Inc.. Secaucus, N.J., USA.

Zaccarian, L., D. Neˇsi´c and A.R. Teel (2005). First order
reset elements and the Clegg integrator revisited. In:
American Control Conference. Portland (OR), USA.
pp. 563–568.