An Algorithm for Multi-Realization of Nonlinear MIMO Systems


1 South Tehran Branch, Islamic Azad University, Tehran, Iran.

2 Khajeh Nasir Toosi University of Technology, Tehran, Iran.


This paper presents a theoretical approach to implementation of the “Multi-realization of nonlinear MIMO systems”. This method aims to find state-variable realization for a set of systems, sharing as many parameters as possible. In this paper a special nonlinear multi-realization problem, namely the multi-realization of feedback linearizable nonlinear systems is considered and an algorithm for achieving minimal stably-based multi-realization of a set of nonlinear feedback linearizable systems is introduced. An example that illustrates this algorithm is also presented


[1] D. Liberzon, “Switching in Systems and Control”, Birkhäuser, Boston, 2003.
A. Morse, “Control Using Logic-Based Switching”, in Trends in control: A European perspective, ew Haven, Springer-Verlag, pp.69–113, 1995.
B. Anderson and M. Gevers, “On the Minimality of Feedback Realisations”, International Journal of Control, Vol.37, No.1, pp.145–158, 1983.
T. Kailath, “Linear Systems”, New Jersey: Prentice-Hall Inc, 1980.
A. S. Morse, “Structural Invariants of Linear Multivariable Systems”, SIAM J. Control, Vol.11, No.3, pp.446–465, 1973.
B. Anderson, S. Su and T. Brinsmead, “Multi-realization of Linear Multi-variable Systems”, IEEE Transaction on Circuits and Systems II, Vol.52, No.8, pp.442–446, 2006.
S. W. Su, B.D.O. Anderson, W. Chen and H. Nguyen, “Multi-realization of Nonlinear Systems”, Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp.5901 - 5905, 2009.
A. Isidori, “Nonlinear Control Systems”, New York: Springer-Verlag, 1989.
R. Hermann and A. Krener, “Nonlinear Controllability and Observability”, IEEE Transaction on Automatic Control, Vol.22, No.5, pp.728–740, 1977.