Positivity and Linearization of a Class of Nonlinear Continuous–Time Systems by State Feedbacks

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.Search in Google Scholar

Brockett, R.W. (1976). Nonlinear systems and differential geometry, Proceedings of the IEEE64(1): 61–71.10.1109/PROC.1976.10067Search in Google Scholar

Charlet, B., Levine, J. and Marino, R. (1991). Sufficient conditions for dynamic state feedback linearization, SIAM Journal on Control and Optimization29(1): 38–57.10.1137/0329002Search in Google Scholar

Daizhan, C., Tzyh-Jong, T. and Isidori, A. (1985). Global external linearization of nonlinear systems via feedback, IEEE Transactions on Automatic Control30(8): 808–811.10.1109/TAC.1985.1104040Search in Google Scholar

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.Search in Google Scholar

Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, NewYork, NY.10.1002/9781118033029Search in Google Scholar

Isidori, A. (1989). Nonlinear Control Systems, Springer-Verlag, Berlin.10.1007/978-3-662-02581-9Search in Google Scholar

Jakubczyk, B. (2001). Introduction to geometric nonlinear control: Controllability and Lie bracket, Summer School on Mathematical Control Theory, Triest, Italy.Search in Google Scholar

Jakubczyk, B. and Respondek, W. (1980). On linearization of control systems, Bulletin of the Polish Academy Sciences: Technical Sciences28: 517–521.Search in Google Scholar

Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer Verlag, London.10.1007/978-1-4471-0221-2Search in Google Scholar

Kaczorek, T. (2011). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuit and Systems58(6): 1203–1210.10.1109/TCSI.2010.2096111Search in Google Scholar

Kaczorek, T. (2012). Selected Problems of Fractional System Theory, Springer Verlag, Berlin.10.1007/978-3-642-20502-6Search in Google Scholar

Kaczorek, T. (2013). Minimum energy control of fractional positive discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences61(4): 803–807.10.2478/bpasts-2013-0087Search in Google Scholar

Kaczorek, T. (2014a). Minimum energy control of descriptor positive discrete-time systems, COMPEL33(3): 1–14.10.1108/COMPEL-04-2013-0111Search in Google Scholar

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 Sciences62(1): 85–89.10.2478/bpasts-2014-0010Search in Google Scholar

Kaczorek, T. (2014c). Minimum energy control of fractional positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science24(2): 335–340, DOI: 10.2478/amcs-2014-0025.10.2478/amcs-2014-0025Search in Google Scholar

Malesza, W. (2008). Geometry and Equivalence of Linear and Nonlinear Control Systems Invariant on Corner Regions, Ph.D. thesis, Warsaw University of Technology, Warsaw.Search in Google Scholar

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.Search in Google Scholar

Marino, R. and Tomei, P. (1995). Nonlinear Control Design— Geometric, Adaptive, Robust, Prentice Hall, London.Search in Google Scholar

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.Search in Google Scholar

Taylor, J.H. and Antoniotti, A.J. (1993). Linearization algorithms for computer-aided control engineering, Control Systems Magazine13(2): 58–64.10.1109/37.206986Search in Google Scholar

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.Search in Google Scholar