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Abstrakty
An LMI approach to investigating the stability and related problems for linear three-dimensional discrete systems is described. The stability and lower bounds for stability margins are discussed for all principal three-dimensional state-space models. The particular emphasis is put on the robust stability for the uncertain case. A numerical example is presented to illustrate the results developed in the paper.
Rocznik
Tom
Strony
361--379
Opis fizyczny
1 tabela, bibliogr. 33 poz.
Twórcy
autor
- Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland (Instytut Sterowania i Systemów Informatycznych Uniwersytetu Zielonogórskiego)
autor
- School of Electrical And Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798 Singapore
autor
- Department of Automation, Nanjing University of Science and Technology Nanjing 210094, P. R. China
autor
- Department of Mechanical Engineering, University of Hong Kong Pokfulam Road, Hong Kong
Bibliografia
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- [4] S. Boyd, L. E. Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities in systems and control theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia 1994.
- [5] A. R. C. Crusius, and A. Trofino, Sufficient LMI conditions for output feedback control problems, IEEE Trans. Automat. Control, (1999) 1053-1057.
- [6] C. Du, L. Xie, LMI approach to output feedback stabilisation of 2-D discrete systems, Int. J. Control, 72 (1999) 97-106.
- [7] T. Fernando, H. Trinh, Lower bounds for stability margin of two-dimensional discrete systems using the MaeLaurine series, Computers and Electrical Engineering, 25 (1999) 95-109.
- [8] E. Fornasini, G. Marchesini, Doubly indexe dynamical systems: state-space models and structural properties, Math. Syst. Theory 12 (1978) 59-72.
- [9] K. Galkowski, State-space realizations of multi-input multi-output n-D systems — Elementary operations approach, Int. J. Control, 66 (1997) 119-141.
- [10] K. Galkowski, State-space realizations of linear 20D systems with extensions to the general nD (n > 2) Case, Lecture Notes in Control and Information Sciences, Springer Verlag, London 2001.
- [11] K. Galkowski, E. Rogers, S. Xu, J. Lam, D. Owens, LMIs-a fundamental tool in analysis and controller design for discrete linear repetitive processes, IEEE Trans. Circ. Sys.-I, 49, 6, (2002) 768-778.
- [12] K. Galkowski, J. Wood, Multidimensional signals, circuits and systems, ed.: Taylor and Francis, London 2001.
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- [14] T. Hinamoto, Fornaasini-Marchesini model with no overflow oscillations and its application to 2-D digital filter design, in: Proc. ISCAS’89, (1989) 1680-1683.
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- [17] D. Johnson, E. Rogers, A. Pugh, G. Hayton, D. Owens, A polynomial matrix theory for a certain class ot 2-D linear systems, Linear Algebra and its applications, 241 (1996).
- [18] E. Jury, Stability of multidimensional scalar and matrix polynomial, Proceedings of the IEEE, 66 (1978) 1018-1047.
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- [20] T. Kaczorek, Linear control systems, Research Studies Press LTD, Taunton England, John Wiley, NY 1992.
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- [24] Z. Lin, Feedback stabilization of MIMO 3-D linear systems, IEEE Trans. Automat. Control, 44 (1999) 1950-1955.
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- [26] V. Rajaravivarma, P. K. Rajan, H. C. Reddy, Planar symmetries in 3-D filter response and their application in 3-D filter design, IEEE Trans. Circ. Sys.-II, 39 (1992) 356-368.
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- [31] S. Xu, J. Lam, K. Galkowski, Z. Lin, Lower bounds for stability margins of 2D discrete systems: an LMI approach, Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications Algorithms, to be published.
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Bibliografia
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