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Stability margins for generalized fractional two-dimensional state space models

Salmi Souad, Bouagada Djillali

Archives of Control Sciences

2024

Vol. 34, No. 1

23--37

In this paper, a new class of bidimensional fractional linear systems is considered. The stability radius of the disturbed system is described according to the H∞ norm. Sufficient conditions to ensure the stability margins of the closed-loop system are offered in terms of linear matrix inequalities. The concept of D stability region for these systems is also considered. Examples are provided to verify the applicability of our main result.

Positivity and stability of fractional 2D Lyapunov systems described by the Roesser model

Rogowski K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2011

Vol. 59, nr 2

195-200

A new class of fractional 2D Lyapunov systems described by the Roesser models is introduced. Necessary and sufficient conditions for the positivity and asymptotic stability of the new class of systems are established. It is shown that the checking of the asymptotic stability of positive 2D fractional Lyapunov systems can be reduced to testing the asymptotic stability of corresponding positive standard 1D discretetime systems. The considerations are illustrated by a numerical example.