Abstract
This paper considers stability problems for discrete-time linear fractional -order systems (LFOSs) with Markovian jumps and/ or multiplicative noise. For the case of LFOSs with finite delays and Markovian jumps, we provide sufficient conditions for the mean-square asymptotic (MSA) stability or instability of the system by using Lyapunov type equations. In the absence of the Markovian perturbations, we use Ztransform and operator spectral properties to derive instability criteria for fractional-order systems with multiplicative random perturbations and either finite or infinite delays. Four numerical results accompanied by computer simulations illustrate the effectiveness of the theoretical results.
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