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

Abstract

It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.

New Stability Tests of Positive Standard and Fractional Linear Systems

“…The stability of positive continuous-time linear systems with delays has been addressed in [5]. 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 [6]. The asymptotic stability of positive 2D linear systems without and with delays has been considered in [7,8].…”

Stability of positive fractional 2D linear systems with delays

“…Stability of positive 1D and 2D linear systems has been considered in [5,10,11,26,27] and the robust stability in [2]. The positive fractional linear systems have been addressed in [15][16][17][18] and their stability has been investigated in [3,4,20,21]. LMI approaches to checking the stability of positive 2D systems have been proposed in [12,26].…”

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

“…Variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine, etc.. New stability conditions for discrete-time linear systems have been proposed in (Busłowicz 2008) and next have been extended to robust stability of fractional discretetime linear systems in (Busłowicz 2010). 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).…”