Decentralized stabilization of fractional positive descriptor continuous-time linear systems

Boyd, S. El Ghaoui, L. Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.10.1137/1.9781611970777Search in Google Scholar

Bru, R., Coll, C. and Sanchez E. (2000). About positively discrete-time singular systems, in M.E. Mastorakis (Ed.), System and Control: Theory and Applications, World Scientific and Engineering Society, Athens, pp. 44-48.Search in Google Scholar

Bru, R. Coll, C. Romero-Vivo, S. and Sanchez, E. (2003). Some problems about structural properties of positive descriptor systems, in L. Benvennnuti et al. (Eds.), Positive Systems, Lecture Notes in Control and Information Science, Vol. 294, Springer, Berlin, pp. 233-240.10.1007/978-3-540-44928-7_32Search in Google Scholar

State, N.J. (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constructions, SIAM Journal on Applied Mathematics 31(3): 411-425.10.1137/0131035Open DOISearch in Google Scholar

Caputo, M. and Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1(2): 1-13.Search in Google Scholar

Dai, L. (1989). Singular Control Systems, Springer-Verlag, Berlin. 10.1007/BFb0002475Search in Google Scholar

Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292.10.1016/j.laa.2009.04.024Search in Google Scholar

Duan, G.R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.10.1007/978-1-4419-6397-0Search in Google Scholar

Fahmy, M.M. and O’Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421-1431.10.1080/00207178908559713Open DOISearch in Google Scholar

Farina, L. and Rinaldi, S. (2000). Positive Linear Systems,Wiley, New York, NY.10.1002/9781118033029Search in Google Scholar

Giorgio, G. and Zuccotti, C. (2015). Metzlerian and generalized Metzlerian matrices: Some properties and economic applications, Journal of Mathematics Research 7(2): 42-55.10.5539/jmr.v7n2p42Search in Google Scholar

Kaczorek, T. (1997). Positive singular discrete time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 45(4): 619-631.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. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458.10.2478/v10175-010-0043-1Search in Google Scholar

Kaczorek, T. (2011a). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.10.1007/978-3-642-20502-6Search in Google Scholar

Kaczorek, T. (2011b). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 753-761.Search in Google Scholar

Kaczorek, T. (2012). Positive fractional continuous-time linear systems with singular pencil, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(1): 9-12.10.2478/v10175-012-0002-0Search in Google Scholar

Kaczorek, T. (2013). Application of the Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29-33, DOI: 10.2478/amcs-2013-0003.10.2478/amcs-2013-0003Open DOISearch in Google Scholar

Kaczorek, T. (2014a). Descriptor positive discrete-time and continuous-time nonlinear systems, Proceedings of SPIE 92902Q.10.1117/12.2074558Search in Google Scholar

Kaczorek, T. (2014b). Minimum energy control of fractional descriptor positive discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 24(4): 735-743, DOI: 10.2478/amcs-2014-0054.10.2478/amcs-2014-0054Open DOISearch in Google Scholar

Losada, J. and Nieto, J. (2015). Properties of a new fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1(2) 87-92.Search in Google Scholar

Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY. Search in Google Scholar

Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Ł´od´z University of Technology Press, Ł´od´z, (in Polish).Search in Google Scholar

Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.Search in Google Scholar

Sajewski, Ł. (2016a). Descriptor fractional discrete-time linear system and its solution-Comparison of three different methods, in R. Szewczyk et al. (Eds.), Challenges in Automation, Robotics and Measurement Techniques, Advances in Intelligent Systems & Computing, Vol. 440, Springer, Cham, pp. 37-50.10.1007/978-3-319-29357-8_4Search in Google Scholar

Sajewski, Ł. (2016b). Descriptor fractional discrete-time linear system with two different fractional orders and its solution, Bulletin of the Polish Academy of Sciences: Technical Science 64(1): 15-20.10.1515/bpasts-2016-0003Search in Google Scholar

Van Dooren, P. (1979). The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103-140.10.1016/0024-3795(79)90035-1Search in Google Scholar

Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640-2659. 10.1016/j.laa.2008.03.002Search in Google Scholar