Abstract
In this paper we present two strategies to design a hybrid controller for a system described by several nonlinear vector fields. Besides the overall goal to find a controller that stabilizes the closed-loop hybrid system, the selection will also be made in such a way that an exponentially stable closed-loop system is obtained. The design strategies are based on stated stability and exponential stability theorems for hybrid systems. The first approach results in regions where it is possible to change vector fields guaranteeing (exponential) stability of the closedloop hybrid system. The second design strategy utilizes the fact that a system is (exponentially) stable if it is always possible to choose a vector field that points in a direction such that the trajectory approaches the equilibrium point. These conditions can be verified by solving a linear matrix inequality (LMI) problem.
Preview
Unable to display preview. Download preview PDF.
References
K. J. Åström and B. Wittenmark. Adaptive Control. Addison-Wesley, 1989.
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.
M. Johansson and A. Rantzer. Computation of piecewise quadratic Lyapunov functions for hybrid systems. Technical Report ISRN LUTFD2/TFRT-7549-SE, Department of Automatic Control, Lund Institute of Technology, June 1996.
H. K. Khalil. Nonlinear Systems. Prentice-Hall, 1996.
J. Malmborg, B. Bernhardsson, and K. J. Åström. A stabilizing switching scheme for multi controller systems. In Proc. of 13th IFAC, pages F:229–234, 1996.
S. Pettersson and B. Lennartson. LMI for stability and robustness of hybrid systems. Technical Report I-96/005, Control Engineering Laboratory, Chalmers University of Technology, 1996.
S. Pettersson and B. Lennartson. Stability and robustness for hybrid systems. In Proc. of 35th CDC, Kobe, 1996. To appear.
J.-J. E. Slotine and W. Li. Applied Nonlinear Control. Prentice-Hall, 1991.
H. O. Wang, K. Tanaka, and M. F. Griffin. An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Trans. Fuzzy Systems, 4(1): 14–23, 1996.
M. A. Wicks, P. Peleties, and R. A. DeCarlo. Construction of piecewise Lyapunov functions for stabilising switched systems. In Proc. of the 33rd CDC, pages 3492–97, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pettersson, S., Lennartson, B. (1997). Controller design of hybrid systems. In: Maler, O. (eds) Hybrid and Real-Time Systems. HART 1997. Lecture Notes in Computer Science, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014729
Download citation
DOI: https://doi.org/10.1007/BFb0014729
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62600-8
Online ISBN: 978-3-540-68330-8
eBook Packages: Springer Book Archive