STABILITY CRITERIA FOR STOCHASTIC DISCRETE-TIME FRACTIONAL ORDER SYSTEMS

Abstract

In this paper are discussed stability problems for a class of discrete-time fractional systems (DTFSs) with independent random perturbations. Two notions of mean square stability (MSS) and mean square asymptotic stability (MSAS) are introduced for the DTFSs by using an approximating linear stochastic system. Necessary and sufficient conditions for MSS and MSA are then derived.

Keywords

• Lyapunov type operators
• discrete-time fractional systems
• stochastic stability.