LMI approach to stability of 2D positive systems

Tadeusz Kaczorek1
1Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw, Poland

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Balakrishnan V., Vandenberghe L. (2003). Semidefinite programming duality nad linear time-invariant systems. IEEE Transactions on Automatic Control 48, 30–41

Bose N.K. (1982). Applied multidimensional system theory. New York, Van Nostrand Reinhold Co

Bose N.K., Buchberger B., Guiver J.P. (2003). Multidimensional systems theory and applications. Dordrecht, The Netherlands, Kluwer Academic Publishers

Busłowicz, M. (2006). Stability of positive linear discrete-time systems with unit delay with canonical forms of state matrices. In 12th IEEE International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland.

Farina L., Rinaldi S. (2000). Positive linear systems; theory and applications. New York, Wiley

Fornasini E., Marchesini G. (1976). State-space realization theory of two-dimensional filters. IEEE Transactiona on Automatic Control AC-21: 481–491

Fornasini E., Marchesini G. (1978). Double indexed dynamical systems. Mathematical Systems Theory 12, 59–72

Gałkowski K., Lam J., Xu S., Lin Z. (2003). LMI approach to state-feedback stabilization of multidimensional systems. International Journal of Control 76(14): 1428–1436

Gałkowski K. (2001). State space realizations of linear 2D systems with extensions to the general nD (n >  2) case. London, Springer-Verlag

Kaczorek T. (1985). Two-dimensional linear systems. Berlin, Springer-Verlag

Kaczorek T. (1996). Reachability and controllability of non-negative 2D Roesser type models. Bulletin De L Academie Polonaise Des Sciences-Serie Des Sciences Techniques 44(4): 405–410

Kaczorek T. (2001). Positive 1D and 2D systems. London, Springer-Verlag

Kaczorek T. (2003). Realizations problem for positive discrete-time systems with delays. Systems Science 29(1): 15–29

Kaczorek T. (2004). Realization problem for positive 2D systems with delays. Machine Intelligence and Robotic Control 6(2): 61–68

Kaczorek T. (2005). Reachability and minimum energy control of positive 2D systems with delays. Control and Cybernetics 34(2): 411–423

Kaczorek T. (2006a) Minimal positive realizations for discrete-time systems with state time-delays. The International Journal for Computation and Mathematics in Electrical and Electronics Engineering, COMPEL 25(4): 812–826

Kaczorek, T. (2006b). Positive 2D systems with delays, MMAR 2006. In 12th IEEE IFAC International Conference on Methods in Automation and Robotics, 28–31 August, Poland.

Kaczorek T. (2007). Choice of the forms of Lyapunov functions for positive 2D Roesser model. International Journal of Applied Mathematics and Computer Science 17(4): 471–475

Kaczorek, T. (2008). Asymptotic stability of positive 2D linear systems, Numerical Linear Algebra in Signals, Systems and Control (in press).

Kaczorek, T. (in press). Asymptotic stability of positive 2D linear systems with delays. In XIII Scientific Conference Computer Applications in Electrical Engineering, April 14–16, 2008 Poznan, Poland.

Kurek J. (1985). The general state-space model for a two-dimensional linear digital systems. IEEE Transactions on Automatic Control AC-30: 600–602

Roesser R.P. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control AC-20(1): 1–10

Twardy M. (2007). An LMI approach to checking stability of 2D positive systems. Bulletin De L Academie Polonaise Des Sciences-Serie Des Sciences Techniques 55(4): 385–395

Valcher M.E. (1997). On the internal stability and asymptotic behavior of 2D positive systems. IEEE Transactions On Circuits and Systems – I 44(7): 602–613