Abstract
This paper focuses on master slave synchronization problem of piecewise affine (PWA) systems of continuous type. The synchronization problem is solved as a global asymptotic stability problem of the error dynamics between the master and the slave systems via a state feedback control law. Using a Lyapunov approach and the so-called S-procedure, new sufficient conditions are proposed. The synchronization criteria are formulated as Linear Matrix Inequalities (LMIs) which are efficiently solved via common software. Two engineering systems are finally used to illustrate the efficiency of the proposed approach: A non smooth mechanical system and a non linear electrical circuit. Simulation results prove that the synchronization problem is achieved with success applying the proposed strategy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Nijmeijer, H., Rodriguez-Angeles, A.: Synchronization of mechanical systems. World Scientific Publishing Co. Pte. Ltd, Singapore (2003)
Blekhman, I., Fradkov, A., Nijmeijer, H., Pogromsky, A.Y.: On self synchronization and controlled synchronization. Systems & Control Letters 31, 299–305 (1997)
Rodriguez-Angeles, A., Nijmeijer, H.: Mutual synchronization of robots via estimated state-feedback: a cooperative approach. IEEE Transactions on Control Systems Technology 12, 542–554 (2004)
Curran, P.F., Suykens, J.A.K., Chua, L.O.: Absolute stability theory and master–slave synchronization. International Journal of Bifurcation and Chaos 7, 2891–2896 (1997)
Suykens, J.A.K., Curran, P.F., Chua, L.O.: Master–slave synchronization using dynamic output feedback. International Journal of Bifurcation and Chaos 7, 671–679 (1997)
Suykens, J.A.K., Curran, P.F., Chua, L.O.: Robust synthesis for master-slave synchronization of Lur’e Systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 46, 841–850 (1999)
Nijmeijer, H., Mareels, I.M.Y.: An observer looks at synchronization. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 44, 882–890 (1997)
Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35, 407–427 (1999)
Rodrigues, L., Boyd, S.: Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization. Systems and Control Letters 54, 835–853 (2005)
Rodrigues, L., How, J.: Observer-based control of piecewise-affine systems. International Journal of Control 76, 459–477 (2003)
Hassibi, A., Boyd, S.P.: Quadratic stabilization and control of piecewise-linear systems. In: American Control Conference, pp. 3659–3664. IEEE Press, New York (1998)
Pavlov, A., Pogromsky, A., Van de Wouw, N., Nijmeijer, H.: On convergence properties of piecewise affine systems. International Journal of Control 80, 1233–1247 (2007)
Johansson, M., Rantzer, A.: Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Transactions on Automatic Control 43, 555–559 (1998)
Rodrigues, L., How, J.: Synthesis of piecewise-affine controllers for stabilization of nonlinear systems. In: 42nd IEEE Conference on Decision and Control, pp. 2071–2076. IEEE Press, New York (2003)
Rodrigues, L.: Stability of sampled-data piecewise-affine systems under state feedback. Automatica 43, 1249–1256 (2007)
Van de Wouw, N., Pavlov, A., Nijmeijer, H.: Controlled synchronization of continuous PWA systems. In: Pettersen, K.Y., Gravdahl, J.T., Nijmeijer, H. (eds.) LNCS, vol. 336, pp. 271–289. Springer, Heidelberg (2006)
Van de Wouw, N., Pavlov, A.: Tracking and synchronization for a class of PWA systems. Automatica 44, 2909–2915 (2008)
Pavlov, A., Van de Wouw, N., Nijmeijer, H.: Convergent dynamics, a tribute to B.P. Demidovich. Systems and Control Letters 52, 257–261 (2004)
Slotine, J.J.E., Li, W.: Applied nonlinear control. Prentice-Hall, Englewood Cliffs (1991)
Boubaker, O.: Master-slave synchronization for PWA systems. In: 3rd IEEE International Conference on Signals, Circuits and Systems. IEEE Press, New York (2009)
Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. Studies in Applied Mathematics. SIAM, Philadelphia (1994)
Kailath, T.: Linear systems. Prentice-Hall, Englewood Cliffs (1989)
Van de Wouw, N., Pavlov, A., Pettersen, K.Y., Nijmeijer, H.: Output tracking control of PWA systems. In: 45th IEEE Conference on Decision and Control, pp. 2637–2642. IEEE Press, New York (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mkaouar, H., Boubaker, O. (2011). Sufficient Conditions for Global Synchronization of Continuous Piecewise Affine Systems. In: Kamel, M., Karray, F., Gueaieb, W., Khamis, A. (eds) Autonomous and Intelligent Systems. AIS 2011. Lecture Notes in Computer Science(), vol 6752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21538-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-21538-4_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21537-7
Online ISBN: 978-3-642-21538-4
eBook Packages: Computer ScienceComputer Science (R0)