Asymptotic stability of positive 2D linear systems with delays

Abstract

Abstract. New necessary and sufficient conditions for the asymptotic stability of positive 2D linear systems with delays described by the general model, Fornasini-Marchesini models and Roesser model are established. It is shown that checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to the checking of the asymptotic stability of corresponding positive 1D linear systems without delays. The efficiency of the new criterions is demonstrated on numerical examples.

New Stability Tests Of Positive 1D And 2D Linear Systems

“…In a similar way as for 1D linear systems using (Kaczorek 2009b) the considerations can be easily extended to 2D linear systems with delays and to fractional 1D and 2D linear systems.…”

“…The stability of positive continuous-time linear systems with delays has been addressed in (Kaczorek 2009c) The independence of the asymptotic stability of positive 2D linear systems with delays of the number and values of the delays has been shown in (Kaczorek 2009d). The asymptotic stability of positive 2D linear systems without and with delays has been considered in (Kaczorek 2009a and2009b). The stability and stabilization of positive fractional linear systems by state-feedbacks have been analyzed in (Kaczorek 2010).…”

Stability and stabilization of positive fractional linear systems by state-feedbacks

“…Theorem 18 [16,18]. The positive fractional 2D system (51) is practically stable only if the positive 2D system…”

“…Stability of positive 1D and 2D linear systems has been considered in [10,[14][15][16][17][18] and the robust stability in [19]. Mathematical fundaments of fractional calculus are given in the monographs [20][21][22][23][24][25].…”

Independence of Asymptotic Stability of Positive 2D Linear Systems with Delays of Their Delays

“…Asymptotic stability of positive 2D linear systems was investigated in (Kaczorek, 2009a;2009b;2009c;2008c) and robust stability of positive 1D linear systems in (Busłowicz, 2007;.…”