New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators

الملخص EN

This paper provides new results on a stable discretization of commensurate fractional-order continuous-time LTI systems using the Al-Alaoui and Tustin discretization methods.

New, graphical, and analytical stability/instability conditions are given for discrete-time systems obtained by means of the Al-Alaoui discretization scheme.

On this basis, an analytically driven stability condition for discrete-time systems using the Tustin-based approach is presented.

Finally, the stability of discrete-time systems obtained by finite-length approximation of the Al-Alaoui and Tustin operators are discussed.

Simulation experiments confirm the effectiveness of the introduced stability tests.