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Accessibility conditions of MIMO nonlinear control systems on homogeneous time scales
1. | Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland |
2. | Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia, Estonia |
3. | Faculty of Computer Science, Białystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland |
References:
[1] |
E. Aranda-Bricaire, Ü. Kotta and C. Moog, Linearization of discrete-time systems, SIAM J. Contr. Optim., 34 (1996), 1999-2023.
doi: 10.1137/S0363012994267315. |
[2] |
E. Artin, Geometric Algebra, Interscience Publishers, Inc., New York-London, 1957.
doi: 10.1002/9781118164518. |
[3] |
Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz, M. Tőnso and M. Wyrwas, Algebraic formalism of differential $p$-forms and vector fields for nonlinear control systems on homogeneous time scales, Proc. Estonian Acad. Sci., 62 (2013), 215-226.
doi: 10.3176/proc.2013.4.02. |
[4] |
Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz and M. Wyrwas, Algebraic formalism of differential one-forms for nonlinear control systems on time scales, Proc. Estonian Acad. of Sci. Phys. Math., 56 (2007), 264-282. |
[5] |
J. Belikov, V. Kaparin, Ü. Kotta and M. Tőnso, NLControl website,, 2014. Available from: , ().
|
[6] |
J. Belikov, Ü. Kotta and M. Tőnso, Realization of nonlinear MIMO system on homogeneous time scales, European Journal of Control, 23 (2015), 48-54.
doi: 10.1016/j.ejcon.2015.01.006. |
[7] |
M. Bohner and A. Peterson, Dynamic Equations on Time Scales. An Introduction with Applications., Birkhäuser, Boston, 2001.
doi: 10.1007/978-1-4612-0201-1. |
[8] |
M. Bronstein and M. Petkovšek, An introduction to pseudo-linear algebra, Theoretical Computer Science, 157 (1996), 3-33.
doi: 10.1016/0304-3975(95)00173-5. |
[9] |
R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmitt and P. A. Griffiths, Exterior Differential Systems, Math. Sci. Res. Inst. Publ. 18, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4613-9714-4. |
[10] |
D. Casagrande, Ü. Kotta, M. Tőnso and M. Wyrwas, Transfer equivalence and realization of nonlinear input-output delta-differential equations on homogeneous time scales, IEEE Trans. Autom. Contr., 55 (2010), 2601-2606.
doi: 10.1109/TAC.2010.2060251. |
[11] |
P. M. Cohn, Free Rings and Their Relations, 2nd edition, London Mathematical Society Monographs, 19, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1985. |
[12] |
R. M. Cohn, Difference Algebra, Interscience Publishers John Wiley & Sons, New York-London-Sydeny, 1965. |
[13] |
G. Conte, C. H. Moog and A. M. Perdon, Algebraic Methods for Nonlinear Control Systems. Theory and Applications, 2nd edition, Communications and Control Engineering Series. Springer-Verlag London, Ltd., London, 2007.
doi: 10.1007/978-1-84628-595-0. |
[14] |
Ü. Kotta, Z. Bartosiewicz, S. Nőmm and E. Pawłuszewicz, Linear input-output equivalence and row reducedness of discrete-time nonlinear systems, IEEE Trans. Autom. Contr., 56 (2011), 1421-1426.
doi: 10.1109/TAC.2011.2112430. |
[15] |
Ü. Kotta, Z. Bartosiewicz, E. Pawłuszewicz and M. Wyrwas, Irreducibility, reduction and transfer equivalence of nonlinear input-output equations on homogeneous time scales, Systems and Control Letters, 58 (2009), 646-651.
doi: 10.1016/j.sysconle.2009.04.006. |
[16] |
Ü. Kotta, B. Rehák and M. Wyrwas, Reduction of MIMO nonlinear systems on homogenous time scales, in 8th IFAC Symposium on Nonlinear Control Systems (NOLCOS), University of Bologna, Bologna, Italy, 2010, 1249-1254.
doi: 10.3182/20100901-3-IT-2016.00007. |
[17] |
Ü. Kotta and M. Tőnso, Realization of discrete-time nonlinear input-output equations: Polynomial approach, Automatica, 48 (2012), 255-262.
doi: 10.1016/j.automatica.2011.07.010. |
[18] |
Ü. Kotta, M. Tőnso and Y. Kawano, Polynomial accessibility condition for the multi-input multi-output nonlinear control system, Proc. Estonian Acad. Sci., 63 (2014), 136-150.
doi: 10.3176/proc.2014.2.04. |
[19] |
J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, 30. American Mathematical Society, Providence, RI, 2001.
doi: 10.1090/gsm/030. |
[20] |
M. Ondera, Computer-Aided Design of Nonlinear Systems and their Generalized Transfer Functions, PhD thesis, Slovak University of Technology in Bratislava, 2008. |
[21] |
O. Ore, Theory of non-commutative polynomials, Annals of Mathematics, 34 (1933), 480-508.
doi: 10.2307/1968173. |
[22] |
J.-F. Pommaret, Partial Differential Control Theory. Vol. I. Mathematical Tools; Vol. II Control Systems, Mathematics and Its Applications 530, Kluwer Academic Publishers, Dordrecht, 2001.
doi: 10.1007/978-94-010-0854-9. |
[23] |
V. M. Popov, Some properties of the control systems with irreducible matrix-transfer functions, Differential Equations and Dynamical Systems, II (Univ. Maryland, College Park, Md., 1969), 169-180. Lecture Notes in Math., 144, Springer, Berlin, 1970. |
[24] |
A. J. van der Schaft, On realization of nonlinear systems described by higher-order differential equations, Mathematical Systems Theory, 19 (1987), 239-275.
doi: 10.1007/BF01704916. |
[25] |
J. C. Willems, The behavioral approach to open and interconnected systems, IEEE Control Systems Magazine, 27 (2007), 46-99.
doi: 10.1109/MCS.2007.906923. |
show all references
References:
[1] |
E. Aranda-Bricaire, Ü. Kotta and C. Moog, Linearization of discrete-time systems, SIAM J. Contr. Optim., 34 (1996), 1999-2023.
doi: 10.1137/S0363012994267315. |
[2] |
E. Artin, Geometric Algebra, Interscience Publishers, Inc., New York-London, 1957.
doi: 10.1002/9781118164518. |
[3] |
Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz, M. Tőnso and M. Wyrwas, Algebraic formalism of differential $p$-forms and vector fields for nonlinear control systems on homogeneous time scales, Proc. Estonian Acad. Sci., 62 (2013), 215-226.
doi: 10.3176/proc.2013.4.02. |
[4] |
Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz and M. Wyrwas, Algebraic formalism of differential one-forms for nonlinear control systems on time scales, Proc. Estonian Acad. of Sci. Phys. Math., 56 (2007), 264-282. |
[5] |
J. Belikov, V. Kaparin, Ü. Kotta and M. Tőnso, NLControl website,, 2014. Available from: , ().
|
[6] |
J. Belikov, Ü. Kotta and M. Tőnso, Realization of nonlinear MIMO system on homogeneous time scales, European Journal of Control, 23 (2015), 48-54.
doi: 10.1016/j.ejcon.2015.01.006. |
[7] |
M. Bohner and A. Peterson, Dynamic Equations on Time Scales. An Introduction with Applications., Birkhäuser, Boston, 2001.
doi: 10.1007/978-1-4612-0201-1. |
[8] |
M. Bronstein and M. Petkovšek, An introduction to pseudo-linear algebra, Theoretical Computer Science, 157 (1996), 3-33.
doi: 10.1016/0304-3975(95)00173-5. |
[9] |
R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmitt and P. A. Griffiths, Exterior Differential Systems, Math. Sci. Res. Inst. Publ. 18, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4613-9714-4. |
[10] |
D. Casagrande, Ü. Kotta, M. Tőnso and M. Wyrwas, Transfer equivalence and realization of nonlinear input-output delta-differential equations on homogeneous time scales, IEEE Trans. Autom. Contr., 55 (2010), 2601-2606.
doi: 10.1109/TAC.2010.2060251. |
[11] |
P. M. Cohn, Free Rings and Their Relations, 2nd edition, London Mathematical Society Monographs, 19, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1985. |
[12] |
R. M. Cohn, Difference Algebra, Interscience Publishers John Wiley & Sons, New York-London-Sydeny, 1965. |
[13] |
G. Conte, C. H. Moog and A. M. Perdon, Algebraic Methods for Nonlinear Control Systems. Theory and Applications, 2nd edition, Communications and Control Engineering Series. Springer-Verlag London, Ltd., London, 2007.
doi: 10.1007/978-1-84628-595-0. |
[14] |
Ü. Kotta, Z. Bartosiewicz, S. Nőmm and E. Pawłuszewicz, Linear input-output equivalence and row reducedness of discrete-time nonlinear systems, IEEE Trans. Autom. Contr., 56 (2011), 1421-1426.
doi: 10.1109/TAC.2011.2112430. |
[15] |
Ü. Kotta, Z. Bartosiewicz, E. Pawłuszewicz and M. Wyrwas, Irreducibility, reduction and transfer equivalence of nonlinear input-output equations on homogeneous time scales, Systems and Control Letters, 58 (2009), 646-651.
doi: 10.1016/j.sysconle.2009.04.006. |
[16] |
Ü. Kotta, B. Rehák and M. Wyrwas, Reduction of MIMO nonlinear systems on homogenous time scales, in 8th IFAC Symposium on Nonlinear Control Systems (NOLCOS), University of Bologna, Bologna, Italy, 2010, 1249-1254.
doi: 10.3182/20100901-3-IT-2016.00007. |
[17] |
Ü. Kotta and M. Tőnso, Realization of discrete-time nonlinear input-output equations: Polynomial approach, Automatica, 48 (2012), 255-262.
doi: 10.1016/j.automatica.2011.07.010. |
[18] |
Ü. Kotta, M. Tőnso and Y. Kawano, Polynomial accessibility condition for the multi-input multi-output nonlinear control system, Proc. Estonian Acad. Sci., 63 (2014), 136-150.
doi: 10.3176/proc.2014.2.04. |
[19] |
J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, 30. American Mathematical Society, Providence, RI, 2001.
doi: 10.1090/gsm/030. |
[20] |
M. Ondera, Computer-Aided Design of Nonlinear Systems and their Generalized Transfer Functions, PhD thesis, Slovak University of Technology in Bratislava, 2008. |
[21] |
O. Ore, Theory of non-commutative polynomials, Annals of Mathematics, 34 (1933), 480-508.
doi: 10.2307/1968173. |
[22] |
J.-F. Pommaret, Partial Differential Control Theory. Vol. I. Mathematical Tools; Vol. II Control Systems, Mathematics and Its Applications 530, Kluwer Academic Publishers, Dordrecht, 2001.
doi: 10.1007/978-94-010-0854-9. |
[23] |
V. M. Popov, Some properties of the control systems with irreducible matrix-transfer functions, Differential Equations and Dynamical Systems, II (Univ. Maryland, College Park, Md., 1969), 169-180. Lecture Notes in Math., 144, Springer, Berlin, 1970. |
[24] |
A. J. van der Schaft, On realization of nonlinear systems described by higher-order differential equations, Mathematical Systems Theory, 19 (1987), 239-275.
doi: 10.1007/BF01704916. |
[25] |
J. C. Willems, The behavioral approach to open and interconnected systems, IEEE Control Systems Magazine, 27 (2007), 46-99.
doi: 10.1109/MCS.2007.906923. |
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