Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks

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1. Aguilar, J.L.M., Garcia, R.A. and D'Attellis, C.E. (1995). Exact linearization of nonlinear systems: Trajectory tracking with bounded control and state constrains, 38th Midwest Symposium on Circuits and Systems, Rio de Janeiro, Brazil, pp. 620-622. 
2. Brockett, R.W. (1976). Nonlinear systems and differential geometry, Proceedings of the IEEE 64(1): 61-71. 
3. Charlet, B., Levine, J. and Marino, R. (1991). Sufficient conditions for dynamic state feedback linearization, SIAM Journal on Control and Optimization 29(1): 38-57. Zbl0739.93021
4. Daizhan, C., Tzyh-Jong, T. and Isidori, A. (1985). Global external linearization of nonlinear systems via feedback, IEEE Transactions on Automatic Control 30(8): 808-811. Zbl0666.93054
5. Fang, B. and Kelkar, A.G. (2003). Exact linearization of nonlinear systems by time scale transformation, IEEE American Control Conference, Denver, CO, USA, pp. 3555-3560. 
6. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. Zbl0988.93002
7. Isidori, A. (1989). Nonlinear Control Systems, Springer-Verlag, Berlin. Zbl0693.93046
8. Jakubczyk, B. (2001). Introduction to geometric nonlinear control: Controllability and Lie bracket, Summer School on Mathematical Control Theory, Triest, Italy. Zbl1017.93034
9. Jakubczyk, B. and Respondek, W. (1980). On linearization of control systems, Bulletin of the Polish Academy Sciences: Technical Sciences 28: 517-521. Zbl0489.93023
10. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer Verlag, London. Zbl1005.68175
11. Kaczorek, T. (2011). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuit and Systems 58(6): 1203-1210. 
12. Kaczorek, T. (2012). Selected Problems of Fractional System Theory, Springer Verlag, Berlin. 
13. Kaczorek, T. (2013). Minimum energy control of fractional positive discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 61(4): 803-807. 
14. Kaczorek, T. (2014a). Minimum energy control of descriptor positive discrete-time systems, COMPEL 33(3): 1-14. 
15. Kaczorek, T. (2014b). Necessary and sufficient conditions for minimum energy control of positive discrete-time linear systems with bounded inputs, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(1): 85-89. 
16. Kaczorek, T. (2014c). Minimum energy control of fractional positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science 24(2): 335-340, DOI: 10.2478/amcs-2014-0025. Zbl1293.49042
17. Malesza, W. (2008). Geometry and Equivalence of Linear and Nonlinear Control Systems Invariant on Corner Regions, Ph.D. thesis, Warsaw University of Technology, Warsaw. 
18. Malesza, W. and Respondek, W. (2007). State-linearization of positive nonlinear systems: Applications to Lotka-Volterra controlled dynamics, in F. Lamnabhi-Lagarrigu et al. (Eds.), Taming Heterogeneity and Complexity of Embedded Control, John Wiley, Hoboken, NJ, pp. 451-473. 
19. Marino, R. and Tomei, P. (1995). Nonlinear Control Design - Geometric, Adaptive, Robust, Prentice Hall, London. Zbl0833.93003
20. Melhem, K., Saad, M. and Abou, S.C. (2006). Linearization by redundancy and stabilization of nonlinear dynamical systems: A state transformation approach, IEEE International Symposium on Industrial Electronics, Montreal, Canada, pp. 61-68. 
21. Taylor, J.H. and Antoniotti, A.J. (1993). Linearization algorithms for computer-aided control engineering, Control Systems Magazine 13(2): 58-64. 
22. Wei-Bing, G. and Dang-Nan, W. (1992). On the method of global linearization and motion control of nonlinear mechanical systems, International Conference on Industrial Electronics, Control, Instrumentation and Automation, San Diego, CA, USA, pp. 1476-1481.