EXPONENTIAL DICHOTOMY OF DISCRETE TIME LINEAR SYSTEMS WITH MARKOVIAN JUMPS AND INDEPENDENT RANDOM PERTURBATIONS - Viorica Mariela UNGUREANU; Carmen Iuliana BĂRBĂCIORU (Fiabilitate şi Durabilitate)
This paper discuses exponential dichotomy problems for a class of discrete-time systems affected by both Markovian jumps and independent random perturbations. Exponential dichotomy is a type of conditional stability which involves the decomposition of the state space of the system into stable and unstable subspaces. By using the solution representations from [3], we provide two necessary and sufficient conditions for the uniform exponential dichotomy of the stochastic systems. These conditions are completely deterministic and easy to check as it is proved by the final example, which illustrates the effectiveness of the theory